I have the same question as the guy befor me.
I just bought a 2003 galant with the exact same problem.
Ill start it, It sounds fine. I turn the air on and it squeels like a #$%^. Then ill turn the air back off and its fine again.
After its drivein for awhile and drivein lightly the sound stops.
Ive got 1 new belt and one old belt.
Timeing belt and serpintine.
Not sure which is which.
So in my opinion, i think its the belt that turns the ac compressor.
After i replace that ill repost and tell yall if it fixed it.