Did this just happen or was it like this when you bought the car? It appears there could be a couple of issues. Either- the radio is actually toast, or the programming is hosed up somehow. I wouldn't just start throwing money and parts at the situation without knowing for sure what caused the problem. I mean, why was it parked for 3 years? Was this the reason?
In that regard, I think it would be wise to have a dealer look at it and troubleshoot. It may be a little pricey to do, but it'd be worth it to me to know for sure what gremlin is causing the issues. You don't want to play with electrical gremlins.
That's my advice.
2010 2SS/RS Auto, Sunroof, Engine Cover. Transformer Edition package.
2013 ZL1 ragtop #5478. 1 of 54 CRT M6 'verts.