I had to completely reinstall TS3, but I can't until I uninstall everything. I can't uninstall the base game and Seasons, everything else did fine. Going into Control Panel, then Programs and Features (which worked for my other EPs) won't work. I thought restarting my computer might help, but it didn't.

What do you mean it won't work? What is the error message?

You could try another program for uninstalling. I use a free program called CCleaner, it has an option to uninstall programs under "Tools" and also an option to clean up your registry afterwards. Never had a problem with it.

When I click to uninstall, it will instantly pop up saying the program has been uninstalled, but it still shows up as installed. It won't let me reinstall TS3 either, because it still shows up as installed.

Ok, try CCleaner then. The reason that it still might show as installed is probably because there are some traces in the registry. Don't worry, it's free and I've been using it for years with no ill effects. Generally, I would uninstall the basegame last.