The passenger side rear power window will not close the other three windows are workinf fine. The car is a 2005 PT Cruiser

Changing a battery should not affect the power window. The computer will be reset when the battery is disconnected. Sounds like a coincidence. Try banging on the door while operating the window switch to see if it will work again. If not, the door will have to be disassembeled for testing/inspection

electric windows
check fuses any time any electrics fail. first.
and battery if many things fail. (like wont run)

Sounds like a fuse. Find the fuse box when you visit Autozone and get the fuse replaced.

Check the switch, swop the switch with the one for the drivers window, if that works it you need a new switch, if not its door card off and test out the motor and power feeds

Un hook the battery wait 15 min it should work

This sounds like the window motor is bad, try holding the switch in the up or down postion and bang on the inside of the door panel and if the window moves then you will know its the motor, the motor is the most common problem but testing would be nice to make sure, you would need to remove the door panel and with a test light test at the connector that plugs into motor,

Check fuse.

There are 2 or 3 metal fitter that holds the window in place, you can replace them yourself, Are go to a place that install /fix windows. Or check the switch, make sure it not sticking.

REAR - SEDAN ONLY

1. Disconnect and isolate the battery negative cable.
2. Using a trim stick or equivalent, gently pry at the top of the switch.
3. Remove switch and disconnect electrical harness connectors.

try wiggling rear switch located behind seat on center counsel .hope this helps it diffently a switch problem.i have one this happend to me