To diagnose problems with Thunderbird, try one of the following:

• Restart Thunderbird with add-ons disabled (Thunderbird Safe Mode). On the Help menu, click on "Restart with Add-ons Disabled". If Thunderbird works like normal, there is an Add-on or Theme interfering with normal operations. You will need to re-enable add-ons one at a time until you locate the offender.
• Restart the operating system in safe mode with Networking. This loads only the very basics needed to start your computer while enabling an Internet connection. Click on your operating system for instructions on how to start in safe mode: Windows 8, Windows 7, Windows Vista, Windows XP, OSX

If safe mode for the operating system fixes the issue, there's other software in your computer that's causing problems. Possibilities include but not limited to: AV scanning, virus/malware, background downloads such as program updates.

OK, this only solved half of my problem. I was able to connect in safe mode, but now how do I determine what software is causing the problem? I have an anti-malware program which I ran and it did find and quarantine three issues, but I'm still unable to connect unless I'm in safe mode. So, any advice on where to go from here?

Thanks!

Which safe mode worked?

If Thunderbird, just make the changes permanent in the dialog as Thunderbird starts then re enable add-ons until you find one that causes the issue.

If it is the windows safe mode it is almost certainly part of your anti virus program, quite probably the firewall component.

Thank you for your follow up reply, but it still doesn't help. It was the windows safe mode that I was able to get in, so I tried disabling my firewall temporarily just to see if that would work and it did not. I don't know what to do next or even how to go about troubleshooting from here.

OK, here is something that may be a piece to the puzzle. A couple of weeks ago my web browsers quit working, both Firefox and Explorer said that they couldn't connect to the Internet even though I had a very strong connection and was getting my emails fine. The advice I got online was to do a system restore, so I did and that worked. For about a week everything was fine, then Thunderbird quit working, saying that the connection was being refused. So, I went through all the diagnostic stuff that was advised here and really didn't get anywhere, so I thought maybe I'd do another system restore. When I got into the control panel to do that, I saw that there was an option to undo the previous restore, so I tried that first. Undoing the previous restore allowed Thunderbird to work again, but then the browsers wouldn't work. So! I did another system restore and am back to being able to access the Internet on my browsers, but not being able to use Thunderbird. Thunderbird says that it has the latest version installed, but (without uninstalling) I installed it again. That did nothing at all. Any thoughts or direction?

What anti virus package are you using?

What version of internet explorer? I suggest you try a repair install of that.

Unfortunately system restore is widely touted as a cure all. My experiences here indicate using it is like Russian roulette. It might work, or it might blow your brains out and is a last resort.

You originally had a problem, system restore moved it and muddied the waters with no suggestion as to the original cause. One probable option is malware. It gets into the TCP/IP stack of windows and works as a firewall and makes sure anti virus programs do not detect it's communications because it is as to low a level. They also often block ports. I suggest you go to one of the major anti virus program web sites (not your installed product) and run their online scan.

An interesting point here is that the error message you first posted is Thunderbird trying to get a web page in the same manner as a web browser.

If you have a product from Symantec, examine the firewall component and verify the versions of programs allowed and ensure the current Thunderbird version has full access.