have you checked the fuse for the lighter socket, if someone has scotched locked the main power for the radio from this it would explain why the unit works from a plug in booster and not the ignition.
Mines fixed!!! i took it to a garage and even though one of the fuses looked alright it was still faulty! try changing your fuses to a new set!
Getting new speakers fittted in it in the next 2 days!
Hope you get it sorted!
Thanks everyone for your help.