Usually the first thing I check is for user-end errors. Usually found between the keyboard and the chair. However, this problem sounds like you should hope that your laptop is under warranty.
The earlier suggestion of trying earphones could narrow it down to the speakers or the sound card itself. The thing is, it's a Compaq which means it's the lowest cost laptop model HP sells to my knowledge and that could be the problem right there (no offense - this is merely fact). If it's under warranty/protection plan, give them a call and talk to them.
you say 1/100 chance of working - I assume this means that the speakers work perfectly as they should on rare occasions? That would imply a hardware issue. Does the sound cut in and out or does this seem to vary depending on how long you're logged in/restarted? (Order of repair operations: Users, Software Hardware so let's break it down).
You said you used all keyboard and sysem options to mdulate the volume and this does not change the status of the problem.
You said reinstalling the driver was not successful - I'm assuming you did this from an Administrator privelaged account? Also, a veritable panacea is to restart into safe mode and then restart and log in normally. I could start an evangelist revival show with how many times that method has worked.
With all user and software issues cleared, either learn to enjoy the sounds of a laptop's one-handed clap, buy a new laptop, or be a lucky soul that managed to have a problem while it's protected.
