Are you trying to install on both profiles or just the one?

Just one. I really only use one profile.

I suggest disabling the password off the profile try to install Thunderbird again and once it is working re-enable the password for the account. If you need more info on how to do this please let me know what operating system you are using.

Thank you. I would love more instruction on how to do this. I'm using Windows 8.1.

ok go to settings ->change pc settings->users->change pasword-> type in current password then when it prompts you to enter new password leave blank click finish and reboot then try to install Thunderbird.

I tried the above and it didn't work. What I get after extracting is as "Run As" window that wants me to use the Administrator account. But I don't have an "Administrator" account, I have profiles that are designated as Administrator. I deleted the profile I don't use, then made the password blank for my only remaining user profile. But the "Run As" window doesn't allow me to have a blank password.

Ok, so when you get run as admin it still prompts you for the password ?

If so you then you may have to boot in safe mode with networking, that way it should be disabled as well. If this is the case can you tell me if you're using a desktop or laptop computer?

If it does not prompt for the password when you click on run as admin then it should allow you to continue with the install.

Please let me know

It does prompt me for password with Administrator. So how do I reboot in Safe Mode? I use a laptop. ... Thank you!

To boot in safe mode you have to reboot your computer as soon as it starts to turn back on you are going to hit either f8 or f12 and you should have an option for safe mode with networking use your arrow keys to move up or down to select it, hit enter if it asks you to select version of windows there should only be one just hit enter again. Once your back to your screen try to install again. If you are able to after install restart again and boot as usual.

Hitting F8 isn't working (tried multiple times, both holding down the key, and tapping it during restart) and F12 doesn't give me the option Safe Mode.

The normal behavior would be to get a UAC prompt, which you need to confirm.

The behavior you describe typically is seen on corporate computers which are locked down due to policies being applied by IT.

So you might ask in a Windows forum, or contact your IT folks.

At this stage this isn't a Thunderbird problem.