Update: I've decided to buy a 'new' motor from the local autoparts store. I was told it would be $130 w/o the $30 core charge. So as I started taking the motor out of the window and apart, I decided to read this thread again and see what others have posted regarding the tricks.
I saw right away the two spring loaded contacts which were caked with some kind of dry grease or carbon buildup or something. The motor was also dirty from the soot from inside that sleeve. I cleaned everything again, this time taking care to be sure I get those 2 contacts cleaned.
Clean side that worked well when pressed:
Dirty side that needed more attention:
As you can see, there's a difference between those two contacts. One looks to be in good shape while the other seems corroded.
I took a frontal shot to allow for better comparison. Mind you these pics are after I cleaned everything with electrical connection cleaner spray.