Quake 3 was working fine on my computer (patched with the latest point release and all) until just now today. Every single time now I try and start the game up, it will freeze during the id intro cinematic. And I mean "freeze" and not "crash" as it stays there and I can't use the Task Manager or Start Menu when hitting Ctrl+Alt+Delete, forcing me to shut down my laptop when a prompt comes up for me to choose the task manager (I'm using Windows 10).

Has anyone else had this problem, and knows how to fix it?

Possible bad sectors on the harddrive. Can be tested a number of ways including copying the Q3 files to a new location. If you can not copy, you have bad sectors. A disc scan would be recommended along with a backup.

Another option maybe failing video card or driver's or RAM (system or video card).

Could also be as simple as a damaged Q3 config file. Can be tested by removing them all. Test by moving them all to a different folder before starting.

I moved the Quake 3 Folder around, and still got the same result. Would reinstalling the game help?

Move is not the same as copy unless you moved the files to a new drive or partition (not folder) on a drive. Which did you do?

I copied the Quake 3 Arena folder from Program Files (x86) to Program Files and now it works fine. What I did originally was just move them.

If that is the case, I would recommend a back up as soon as possible followed by a drive scan for bad sectors.