How do you repair a moonroof in a Mitsubishi 2002 Galant that won't open and just makes noise as you try to open it?

If it is still under warranty, take it to the dealer and get it replaced. It probably isn't repairable and even if it was it would never work properly. Not to mention the fact that you would have to tear apart half your interior. You'd need to take out the headliner and find out exactly where the sunroof is malfunctioning, probably the motor is missing the cables and grinding them away. Then you need to replace whatever is wrong, which entails pulling the moonroof out of the car and tearing it to pieces and then putting it back together again timed correctly.