There are 4 power feeds that go to the radio. It sounds like the one that supplies constant power to keep the memory alive has blown a fuse. These are the four power feeds:
1. Switched to supply power when the ignition is in the ON position or the ACC position. (This appears to be OK if the radio works when the car is running)
2. A power feed that connects to the parking lights and dimmer circuit. (You can check this by turning on the park lights and see if the light in the radio comes on. This should work without turning on the jeep.)
3. A circuit that goes through Fuse #1 (by the battery) and then Fuse #8 (probably in the fuse panel that is accessable when the passenger front door is open.) Check to see if these fuses are OK. If the power locks work, this circuit is probably OK.
4. I can't find the fuse source for the 4th circuit in my wiring diagram but it is connected to the same source as the courtesy lamp switch. Again check the fuses by the passenger door.
I hope this helps you track down your problem.
2000 Jeep Grand Cherokee V8 Stock
93 YJ I6 hard top (really belongs to SPEED)
RE 4.5" Extreme Duty Lift, Advanced Adapters SYE, Tom Woods CV Drive Shaft, EA589 10" rims with 33" x 12.5" MT/Rs
Bullet Proof Front and Rear Bumpers and Tow bar