I had a similar issue - but no heat out of both sides
First to check the operation (you cant really tell by just removing the motor) by getting the jeep to tell you whats wrong
Press both the AC and re-circ buttons and then with another digit move the left hand dial clockwise - this will illuminate all the segments and go through the error codes
54 and 56 are the two we are looking for - one is passenger and one is drivers side door errors
I have just (today) fixed mine from a kit from good old ebay - replacing the wonderful (yet brittle) plastic ones with proper metal doors
If you have a dremmel (or something like that - maybe a knife with a blow torch would also be handy) budget 3 hours to do it all - instructions and videos are all available online (ie. youtube) and really, it isnt that big a job!
Just glad I have a nice toasty car now ready for the winter!