Does this mean you didn't buy a thumb drive for 10 bucks to make a backup? That was probably because nothing is really of value. Free music is free now as it was when you stol -- er, "borrowed" it from the record companies. You can download again if all else fails. If you got some of this "Internet music" from Youtube, and the same videos are not on Youtube now, that may be because they were ILLEGAL. Youtube staff try to keep out of federal prison by following copyright demands from the record companies.
The HUGE DIFFERENCE between your old PC and the Air is the PC was working and the Air is not ("pretty much fried"), so remove the storage (HDD? SSD? PCIe-based module?) from the Air and install it in an enclosure. Connect that to the iMac and Bob's your uncle.
On the other hand, if the Air is not really "FRIED", tell us the actual startup issue with the Air, so we can fix it.