Now you know (I presume) that everything works from the 3 tags on the PCB which is where we started, the next thing is to prove everything is OK from the slip rings onwards, ie that the PCB is OK. Put a bulb or motor into one wire of your 12v supply so you can use it as a circuit tester, so you can work out which of the 5 slip rings corresponds to the yellow black and blue wires. Put one wire to one rail which you can see on your first photo and test each of the slip rings with the other wire to see which corresponds. Repeat with the other rail and then you can ignore those 2 rings. The 3 rings left connect to the 3 colours and we can presume the black and yellow are OK as you can hear the relay clicking. Test which rings are those between the rings and the tags, the remaining ring is the blue, when you know which rings correspond to the colours do what you did originally to make the relay work first then the motor but from the rings not the tags. If everything works you know the deck is all fine, if not there is a fault with the PCB, which the stuck motor might have damaged.
PS. Clean the rings up with some meths or track cleaning fluid.