Do you go on this adress : https://online1.openbank.com/fi71023/retail/individualLogon when you try to login to your bank ? Does Firefox display this page, or the warning instead ? Or is it after you log in ?

See also:

• https://www.ssllabs.com/ssltest/analyze.html?d=online1.openbank.com

The server only supports SSL3 (insecure and blocked by Firefox) and TLS 1.0

If you get a pop-up message asking to update Firefox or plugins or scanning for malware then such a message is likely a scam and you should never respond to such an alert to avoid getting infected with malware.

• Only update Firefox via "Help > About" or by downloading and installing Firefox from the Mozilla server and never via a pop-up or link on a web page.
• Plugins should only be updated via the plugin itself or by visiting the home page of the plugin.

Do a malware check with several malware scanning programs on the Windows computer. Please scan with all programs because each program detects different malware. All these programs have free versions.

Make sure that you update each program to get the latest version of their databases before doing a scan.

• Malwarebytes' Anti-Malware:
  http://www.malwarebytes.org/mbam.php
• AdwCleaner:
  http://www.bleepingcomputer.com/download/adwcleaner/
  http://www.softpedia.com/get/Antivirus/Removal-Tools/AdwCleaner.shtml
• SuperAntispyware:
  http://www.superantispyware.com/
• Microsoft Safety Scanner:
  http://www.microsoft.com/security/scanner/en-us/default.aspx
• Windows Defender:
  http://windows.microsoft.com/en-us/windows/using-defender
• Spybot Search & Destroy:
  http://www.safer-networking.org/en/index.html
• Kasperky Free Security Scan:
  http://www.kaspersky.com/security-scan

You can also do a check for a rootkit infection with TDSSKiller.

• Anti-rootkit utility TDSSKiller:
  http://support.kaspersky.com/5350?el=88446

See also:

• "Spyware on Windows": http://kb.mozillazine.org/Popups_not_blocked
• https://support.mozilla.org/kb/troubleshoot-firefox-issues-caused-malware

My Kaspersky & Windows Defender are all updated & Kaspersky shows that I am protected from anti-viruses, malware, etc. I only update Kaspersky, plug-ins, etc. in their own websites. I never click on Anything I don't know, & if it says it's Kaspersky, etc. and wants me to update, I go to the web site itself. I Never click on something that just pops up.

Yes, I tried that address, it's the same thing. I type in fnfg.com in my search bar, it takes me the search pages, I pick the one I want "fnfg.com official site" and it takes me to the bank page, I put in my user name & click 'sign in'. That's when that page comes up. I copied & pasted the entire message on my 2nd question. The beginning of it, as you can see on my other entry, is....

"This connection is Untrusted. You have asked Firefox to connect securely to 'online1.openbank.com' but we can't confirm your connection is secure" 

I don't know what else to do.

For my opinion, this is a security problem, not a Firefox problem. Why ? Because you should not have "something that just pops up", in addition to the "security warning" you're dealing with.

First rule : no software can protect you at 100%. It doesn't exist.

You use Kapersky : only the antivirus, or the firewall too ? The first element of security on your computer should be the firewall. The antivirus companies start to make firewall, but they are not as good as the ones of the companies that started by being speciallized in firewall. So forget about Windows firewall, and let's say that Kapersky is maybe not the best firewall you can find. But if it is already installed, that's at least a good point.

Then, do you use all the tools of Kapersky ? http://support.kaspersky.com/10047

Read carrefully Cor-el contribution, you should be able to clean your computer like this. If you want to know if there's an infection, you could also follow the instructions here : https://www.youtube.com/watch?v=FDWD9mhgeno ( http://www.filehippo.com/fr/download_hijackthis ).

What makes me a little uncomfortable in the way you're connecting to your bank : - you don't know really where you are connecting in first place : what is written in the adress bar ? Sometimes, you should type yourself : https://www.firstniagara.com/home.aspx to be sure. Or bookmark it. If your computer is infected, the results of the search bar could be corrupted : do you see what I'm afraid of ? When I see fnfg.com, that is not a https, redirecting you to another website, I see a lot of possibilities for MITM attacks. - the security warning coming AFTER you gave login information : please, go on a friend's computer to change the password. Even if Cor-el is right about SSL3 / TLS 1.0, it's more cautious to do that.