Your PC is *plenty* well-specced enough to download like a T1, and still be able to listen to music and watch movies at the same time - it sounds like the problem is that something is eating up much resources already, and like Church said, maybe some issue to do with disc-caching or the like.
Make sure that your hard-drives have DMA mode enabled:
DMA Mode - Micro$oftAlso, run HiJackThis so we can see how many/what apps that you have running on startup - there maybe some clues there:
Download HiJackThisRun it, and then post the results of your scan on this thread, and I'll have a look over it for you.
A quick and dirty fix for now may be to get Task Manager up, (Cntrl+Alt+Del) + (Alt+T) and put the Run Priority of your music player to 'High'.
Try a different music playing app, like Media Player Classic, or something like that, it may have a different data caching profile or something, and may work better for you, although last I checked (not used WinAmp for donkey's years) WinAmp wasn't a particularly heavy-weight app.
You could also check in the uTorrent Settings, and see if it gives you any options to do with the size of your Disk Write Cache or something along those lines, so that you could try increasing it - I know that Azureus has a setting for doing that.