Which is more likely to damage my system? The system in question has spent 3 years in a college setting.

Running the computer without the northbridge fan.

Removing and re-seating the MB to replace the fan.

I can get the fan to work, but I have to remember to do it. I need to open the side of the case and blast it with a bit of compressed air to get it started. I can replace the fan, but due to an incredibly dumb design, the screws for the fan are on the back of the MB.

Any comments would be appreciated.

LMAO! Dude, get your fan fixed. It's not going to hurt your pc just by taking out your motherboard. It's not heart surgery.

Do fix the fan.

There's always a possibility for your NB chip to burn up and you're fucked because it'll look like every other problem.