You are using the original installation CD for the new PC so there shouldn't be any mismatch of licence key numbers, which could occur if sent as a download and then registered.
The backup, are you sure it is a good one, i.e. have you tried it on the first computer?
The backup CD must be the problem now. Are you sure it is an effective backup?
If you are uncertain.... DON'T try and restore it to anything in case you void that as well.
Assuming the program still works on the original PC try another fresh backup of that.