You could also save all your data and do a system restore from the restore partition (assuming that is what HP set up on your computer). They used to give out system restore disks, but restore partitions are more common these days.
This won’t help if you have a hardware flaw. If the onboard sound chip is fubared, this would be a futile effort. Trying to play sound from a Linux live cd should have shown if it was hardware or a Windows software problem, so if you didn’t get sound while using a Linux cd, it is probably a hardware issue.