Get a voltage tester ( nothing fancy, just a test probe with a built in 12V
light bulb) and test these:

Car radio typically have two (sometimes 3 wire for power:

1. Power for the radio itself, normally goes on and off with ignition
switch
2. Power that is "always" on for keeping "station preset memory"
3. the third, if present is for lighting (connected to dimmer circuit).
The voltage present will vary with the dimmer setting.

Check and verify that these are working as it should.  Nerwe radio have
"non-volatile" memory that keeps preset settings without needing external
power. I don't know if your radio has this kind. I think not.