i know when jarret owned the car he took out the mirror with a mailbox but i didnt have the window problem then. it was like 6 monthts later when the car got shot up and i replaced the window it was doing it.i'm wondering if your mirror section has been bent too much seeing that your rubber is torn. I know my mirror wasn't quite aligned, like someone decided to rest something really heavy on it. It made my window not go up as fast as it should have and i bent it back into the right place a little and that helped my window go up just fine now.
Just wondering if you resolved the problem. It's possible to "bind" the window in the tracks or to have a bent track inside the door. The two vertical tracks have some adjustment available by loosening the the top and bottom bolt of each vertical track. This adjustment allows the front of the glass (A pillar) to be higher than the back (B pillar). I suggest removing the door panel and loosening the four bolts holding the tracks in place and the just slightly loosening the motor bolts. If the window goes all the way up then you know its either an out of adjustment track or a weak motor (used or new motor?).
BTW, you've probably discovered that the black sealant holding the plastic sheet in place will stick to everything: tools, skin, door trim, etc. WD40 takes it right off.