Can I connect an 80 mm Computer Fan directly to electricity?

Of course I am, what were you expecting?

IT

 

Just for future reference the "cabinet" is the "case". The CPU is actually a chip in the computer itself, so when you refer to the case as the CPU it can confuse people a bit. The case door is the part you unscrew and remove.

Unless you have a poor cooling setup to begin with, removing the case door will make it worse. Proper cooling means proper airflow, which is usually cool air in the bottom and hot air out the top. Removing the case door can sometimes cool the CPU better, but then pockets of hot air build up and other things overheat.

If a fan in your case was disconnected, have it reconnected or replaced immediately. Don't accept a sketchy alternative like desk fans. You can hook up many 80mm fans in one computer, there should be plenty of 12V power plugs and 80mm fans are only a few bucks.

Good luck!