You don't mention if the radio is one of the original valve radios or a newer transistor.
If it is transistor it definitely will not work in a positive earth car and may have suffered as a result of connecting it in reverse. Hopefully if it is this variety of radio it will still work. Usually if you connect them in reverse polarity they will blow a fuse or issue forth with some smoke.
The old valve radios are not polarity specific, so I would be looking at the electrical connections. You may have hooked the power up to the dash light circuit or something else equally simple. They use a ******** to change the power from DC To AC. This applies to era correct radios.
I would reverse the polarity of the car if you are concerned about polarity.
