If you have work done by Sony dealer using correct motherboard and you used a Genuine Sony Recovery DVD
you should have no problems reactivating without needing to enter the key
If you have got a copy of Win 8 which is not a Sony version you will need the key which if Microsoft thinks is still in use you will have problems
Ask Sony how much a recovery disk set costs
If you made a Windows Recovery Set before the incident you would get a version which checks it is on the correct Sony motherboard type then activates without needing a key.