I found a web site "sight-n-sound audio" that has a oem am/fm/cd player for about 50$.sound reasonable? Looks like theoriginal, nothing fancy.

 

Your cousin probably did not wire the constant(memory) wire correctly. I am guessing that he connected it to the ignition power source instead. Your constant wire needs to be connected to the the car's constant wire which will read 12v when the ignition is off. That is how it keeps your HU memory when the car is off. It is also possible that you have a defective hu if your wiring is correct.