Cannot shift into park

You really cannot add any detail to that? Try selecting one of these:

1. The shift lever locks in the "park" position like normal, but the transmission is still in "reverse", (or neutral). The engine cannot be restarted unless I shift to...

2. The transmission goes into "park", but the shift lever only goes to "reverse". The engine can be restarted when the shift lever is in "reverse".

3. The shift lever binds or gets stuck in "reverse", and the transmission is in "reverse". The engine will start when I shift to "neutral".

Do the shift indicator, shift lever, and transmission gear all agree in all positions? Was anything done recently that could affect the shifter cable? What gear do you have to shift to for the engine to crank and start?

That is a simple case of the shifter cable is out-of-adjustment. Most GM vehicles have their neutral safety switch on the transmission, so it allows the starter system to work when the transmission is in "park", regardless of where the shift lever is. The cable is often not adjusted correctly after the engine / transmission has been lowered for some other service.