It's possible that you are having a problem with some Firefox add-on that is hindering your Firefox's normal behavior. Have you tried disabling all add-ons (just to check), to see if Firefox goes back to normal?

Whenever you have a problem with Firefox, whatever it is, you should make sure it's not caused by one (or more than one) of your installed add-ons, be it an extension, a theme or a plugin. To do that easily and cleanly, run Firefox in safe mode (don't forget to select Disable all add-ons when you start safe mode). If the problem disappears, you know it's from an add-on. Disable them all in normal mode, and enable them one at a time until you find the source of the problem. See this article for information about troubleshooting extensions and themes and this one for plugins.

If you need support for one of your add-ons, you'll have to contact its author.

If the problem does not disappear when all add-ons are disabled, please tell me, so we can work from there. Please have no fear of following my instructions to the line, as all can be easily undone.

Tried all of that, Firefox still crashes when trying to download files. Firefox is about as vanilla as I can get it without reinstalling, which I can't do because I can't download another installer.

You can also have a problem with anti-virus software.

See also http://kb.mozillazine.org/Unable_to_save_or_download_files

You can try to delete the MRU (Most Recently Used) ComDlg32 registry keys with the regedit.exe program.

Navigate to: HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Explorer\ComDlg32

Delete the subkeys (LastVisitedMRU and OpenSaveMRU).

Be careful with editing the registry as there is no Undo possible: all changes are applied immediately.
You can export key(s) before making changes.