I have the same condition on my 2003 Tahoe where the motor clicked but wouldn't move. Took it apart and sure enough the plastic overmolded gear on the brass hub had split and was binding up the worm gear. I believe GM made a horrible material combination selection by mixing brass and nylon given the different thermal coefficient of the 2 materials, leading the weaker nylon to give up the ghost.
I removed the damaged gear and the motor still wouldn't spin. That's when I realized the accelerator pedal is driven by a cable but has the exact gear mechanism and it's gear was also damaged/split. They are the same part. Initially, when I thought it was just one gear I needed, I was trying to convince myself to spend $100 (part plus shipping + tax) to fix a sort of luxury feature. When that number doubled because there were 2 gears needed I said no way.
At this point, I reasoned that there is virtually no load or "precision adjustment" needed on the mechanism and therefore no need to have a perfect mesh of the gears, I simply made the 4 teeth around the crack (2 teeth on each side of the crack) thinner and lower with an exacto knife. They are nylon and very easy to carve. Now the gears are able to make their way past the driven worm gear (albeit with a minor click). The mechanism works fine and rarely gets adjusted anyway.
Give it a shot because you have nothing to lose and it is easy. I just kept removing a slight mount of material on the 4 teeth on both gears until I got them to move past the worm gear. It was able to be repeatedly tested after removing additional material by simply inserting the gear into the housing to engage the driven worm gear and did not require full reassembly.
Good luck and hope it works for you like it did for me.
