If you use Eset Antivirus, check ssl scanning, try turning it off. If this is the reason, go to Eset forums and look for proper solution or workaround, because turning it off permanently may not be a good idea.

I am using Windows Defender for Antivirus. Tried turning it off but it didn't help so I turned it back on.

try telneting your server telnet yourserver 587 then ask the server some questions, for example as explained here: https://support.microsoft.com/pl-pl/kb/153119

what i mean is to test if you can reach your server manually, then you will know where the problem lies... of course encryption can be the problem too. you can test the connection without encryption, but it may not be responsible to test it in untrusted network. you can test on localhost for example by using hmailserver etc. please treat my reply just as a clue to solution, not complete solution. you have to be careful not to leak your credentials by not using encrypted connections.

Find below the troubleshooting information. (Help/troubleshooting/copy to clipboard)

 Application Basics

   Name: Thunderbird
   Version: 45.4.0
   User Agent: Mozilla/5.0 (Windows NT 10.0; WOW64; rv:45.0) Gecko/20100101 Thunderbird/45.4.0
   Profile Folder: Show Folder

             (Local drive)
   Application Build ID: 20160928132736
   Enabled Plugins: about:plugins
   Build Configuration: about:buildconfig
   Memory Use: about:memory

 Mail and News Accounts
   account2:
     INCOMING: account2, , (none) Local Folders, plain, passwordCleartext

   account4:
     INCOMING: account4, , (imap) mail.batterybattery.ca:143, alwaysSTARTTLS, passwordCleartext
     OUTGOING: , mail.batterybattery.ca:587, alwaysSTARTTLS, passwordCleartext, true

 Crash Reports

 Extensions
   Lightning, 4.7.4, true, {e2fda1a4-762b-4020-b5ad-a41df1933103}
   Mail Summaries, 3.0.2, true, mailsummaries@mozillamessaging.com

 Important Modified Preferences

   Name: Value

     browser.cache.disk.capacity: 358400
     browser.cache.disk.filesystem_reported: 1
     browser.cache.disk.smart_size_cached_value: 358400
     browser.cache.disk.smart_size.first_run: false
     browser.cache.disk.smart_size.use_old_max: false
     dom.apps.reset-permissions: true
     extensions.lastAppVersion: 45.4.0
     font.internaluseonly.changed: false
     font.name.monospace.el: Consolas
     font.name.monospace.x-cyrillic: Consolas
     font.name.monospace.x-unicode: Consolas
     font.name.monospace.x-western: Consolas
     font.name.sans-serif.el: Calibri
     font.name.sans-serif.x-cyrillic: Calibri
     font.name.sans-serif.x-unicode: Calibri
     font.name.sans-serif.x-western: Calibri
     font.name.serif.el: Cambria
     font.name.serif.x-cyrillic: Cambria
     font.name.serif.x-unicode: Cambria
     font.name.serif.x-western: Cambria
     font.size.fixed.el: 14
     font.size.fixed.x-cyrillic: 14
     font.size.fixed.x-unicode: 14
     font.size.fixed.x-western: 14
     font.size.variable.el: 17
     font.size.variable.x-cyrillic: 17
     font.size.variable.x-unicode: 17
     font.size.variable.x-western: 17
     gfx.crash-guard.glcontext.appVersion: 45.4.0
     gfx.crash-guard.glcontext.deviceID: 0x22b1
     gfx.crash-guard.glcontext.driverVersion: 10.18.15.4248
     gfx.crash-guard.glcontext.gfx.driver-init.direct3d11-angle: true
     gfx.crash-guard.glcontext.gfx.driver-init.webgl-angle: true
     gfx.crash-guard.glcontext.gfx.driver-init.webgl-angle-force-d3d11: false
     gfx.crash-guard.glcontext.gfx.driver-init.webgl-angle-force-warp: false
     gfx.crash-guard.glcontext.gfx.driver-init.webgl-angle-try-d3d11: true
     gfx.crash-guard.status.glcontext: 2
     mail.openMessageBehavior.version: 1
     mail.winsearch.firstRunDone: true
     mailnews.database.global.datastore.id: cd70b833-4150-4fcc-916c-1eaa170d572
     mailnews.database.global.views.conversation.columns: {"threadCol":{"visible":true,"ordinal":"1"},"flaggedCol":{"visible":true,"ordinal":"3"},"attachmentCol":{"visible":false…
     mailnews.database.global.views.global.columns: {"threadCol":{"visible":true,"ordinal":"1"},"flaggedCol":{"visible":true,"ordinal":"3"},"attachmentCol":{"visible":false…
     network.cookie.prefsMigrated: true
     network.predictor.cleaned-up: true
     places.database.lastMaintenance: 1478784003
     places.history.expiration.transient_current_max_pages: 104858
     plugin.importedState: true
     print.printer_SEC30CDA7AA0BDF.print_bgcolor: false
     print.printer_SEC30CDA7AA0BDF.print_bgimages: false
     print.printer_SEC30CDA7AA0BDF.print_duplex: -437918235
     print.printer_SEC30CDA7AA0BDF.print_edge_bottom: 0
     print.printer_SEC30CDA7AA0BDF.print_edge_left: 0
     print.printer_SEC30CDA7AA0BDF.print_edge_right: 0
     print.printer_SEC30CDA7AA0BDF.print_edge_top: 0
     print.printer_SEC30CDA7AA0BDF.print_evenpages: true
     print.printer_SEC30CDA7AA0BDF.print_footercenter:
     print.printer_SEC30CDA7AA0BDF.print_footerleft: &PT
     print.printer_SEC30CDA7AA0BDF.print_footerright: &D
     print.printer_SEC30CDA7AA0BDF.print_headercenter:
     print.printer_SEC30CDA7AA0BDF.print_headerleft: &T
     print.printer_SEC30CDA7AA0BDF.print_headerright: &U
     print.printer_SEC30CDA7AA0BDF.print_in_color: true
     print.printer_SEC30CDA7AA0BDF.print_margin_bottom: 0.5
     print.printer_SEC30CDA7AA0BDF.print_margin_left: 0.5
     print.printer_SEC30CDA7AA0BDF.print_margin_right: 0.5
     print.printer_SEC30CDA7AA0BDF.print_margin_top: 0.5
     print.printer_SEC30CDA7AA0BDF.print_oddpages: true
     print.printer_SEC30CDA7AA0BDF.print_orientation: 0
     print.printer_SEC30CDA7AA0BDF.print_page_delay: 50
     print.printer_SEC30CDA7AA0BDF.print_paper_data: 1
     print.printer_SEC30CDA7AA0BDF.print_paper_height: 11.00
     print.printer_SEC30CDA7AA0BDF.print_paper_name:
     print.printer_SEC30CDA7AA0BDF.print_paper_size_type: 0
     print.printer_SEC30CDA7AA0BDF.print_paper_size_unit: 0
     print.printer_SEC30CDA7AA0BDF.print_paper_width: 8.50
     print.printer_SEC30CDA7AA0BDF.print_resolution: -437918235
     print.printer_SEC30CDA7AA0BDF.print_reversed: false
     print.printer_SEC30CDA7AA0BDF.print_scaling: 1.00
     print.printer_SEC30CDA7AA0BDF.print_shrink_to_fit: false
     print.printer_SEC30CDA7AA0BDF.print_to_file: false
     print.printer_SEC30CDA7AA0BDF.print_unwriteable_margin_bottom: 0
     print.printer_SEC30CDA7AA0BDF.print_unwriteable_margin_left: 0
     print.printer_SEC30CDA7AA0BDF.print_unwriteable_margin_right: 0
     print.printer_SEC30CDA7AA0BDF.print_unwriteable_margin_top: 0

 Graphics

     Adapter Description: Intel(R) HD Graphics
     Vendor ID: 0x8086
     Device ID: 0x22b1
     Adapter RAM: Unknown
     Adapter Drivers: igdumdim64 igd10iumd64 igd10iumd64 igd12umd64 igdumdim32 igd10iumd32 igd10iumd32 igd12umd32
     Driver Version: 10.18.15.4248
     Driver Date: 8-4-2015
     Direct2D Enabled: false
     DirectWrite Enabled: false (10.0.14393.351)
     ClearType Parameters: Gamma: 2200 Pixel Structure: R ClearType Level: 100 Enhanced Contrast: 200
     WebGL Renderer: Google Inc. -- ANGLE (Intel(R) HD Graphics Direct3D11 vs_5_0 ps_5_0) -- OpenGL ES 2.0 (ANGLE 2.1.0.316930d51ea9)
     GPU Accelerated Windows: 0

     AzureCanvasBackend: skia
     AzureSkiaAccelerated: 0
     AzureFallbackCanvasBackend: cairo
     AzureContentBackend: cairo

 JavaScript

 Incremental GC: 1

 Accessibility

   Activated: 0
   Prevent Accessibility: 0

 Library Versions

     Expected minimum version
     Version in use

     NSPR
     4.12
     4.12

     NSS
     3.21.1 Basic ECC
     3.21.1 Basic ECC

     NSS Util
     3.21.1
     3.21.1

     NSS SSL
     3.21.1 Basic ECC
     3.21.1 Basic ECC

     NSS S/MIME
     3.21.1 Basic ECC
     3.21.1 Basic ECC

I am reading the instruction regarding contacting the server via telnetting.

the telnet command is not recognized by my computer. Following the instructions to install the app I cannot find the app. However, the mail service is working with my phone and all (two) other computers on my local network. I don't think it is a problem at the other end. My other computers are also using Thunderbird.

Your domain for mail servers is ok, mail.batterybattery.ca is in MX record for your domain. Server IP is 209.15.208.71.

I just tried telnet your provider, but it doesn't respond on 587 (like it was filtered). Tried other ports and they seem fine.

Try using SSL and port 465 instead of 587 and tls.

By the way, in Windows if you go into programs and functions / windows features, then on the list you can select telnet to install it. Sorry missed that :)

Thanks a bunch. SSL and Port 465 solved it. Installed telnet as well.