OK, at that point I'm not sure what it could be. If it won't even install then that seems to point at debris from the previous installation. Not all uninstallers actually
remove stuff as completely as they should, sometimes they leave stuff behind that they shouldn't have.
Step 1: Close
every single program that you have running, then temporarily disable your antivirus protection (especially if you use AVG, which is a real asshole about STO for some reason). You don't want to be fighting with mindlessly overzealous AV software while you're trying to fix something.
Step 2: Bring up Task Manager with CTL-ALT-DEL and look for a process called CrypticError.exe. It's their useless crash reporter, which will interfere with any subsequent attempt to launch, load or alter the game files in any way. If you see it, right-click it and end the process. If you don't see it, good -- move to the next step.
Step 3:
Go to Control Panel and uninstall both Arc and STO again (don't use the Arc uninstaller in the program folder), then go into your Program Files (x86) folder and
visually confirm the uninstall. As long as you don't see an Arc folder (and/or a Star Trek Online_en folder) after the uninstall runs, then you've confirmed the full uninstall. If you do see the folder even after running the Control Panel uninstall, you'll want to
force-delete that folder by highlighting the folder then pressing SHIFT-DEL. You should see a Windows popup asking if you're sure you want to permanently delete it, click Yes.
Step 4: Empty the Windows Recycle Bin just to be sure it's all really gone, then reboot Windows before attempting to reinstall. Rebooting will also re-enable your AV software.
Once you're logged back into Windows, you can
retry the Arc download and install from the "Play for Free" button on the website again. Otherwise (and I can't speak for this personally), a lot of people say that installing STO from Steam works for them.
If all that still fails, then you're stuck contacting Arc support and hoping they're not as useless as they usually are. Good luck.