I was hit in the rear and the mechanism that releases the rear hatch is broken. Is there a manual way to pop the window open?

Hmmm tough one, mine is a 2000 and the rear window opens by pushing in the lock other than that it doesn't have a way of opening that I know of, my Rodeo also opens up car door style/swinging to the left, there are probably other variations. Maybe you can see about tearing apart the plastic molding on the inside and getting to the works of it. I've had to do that on other veichles when an interior part of a door broke.
Or try this go to a locksmith and see if he can jimmy the window open or lock, whatever then from there you should be able to tear apart what you need to to fix what's broken. Good Luck. TT

Think Ouside the Box