I suspect that issue is likely with my Realtek audio drivers. I attempted to update / reinstall the Realtek Drivers but now every time I try to install the latest drivers I get an error message when the progress bar is 95% full. My old USB speakers still work but in the device manager the Sound Controller is listed as a generic "High Definition Audio Device".
The only other possibilities I can think of is that my 3.5mm audio jacks are faulty (although I have successfully gotten sound from headphones in the past, I recall it was a bit of a pain to get them working and I don't remember exactly what I did) or that my new speakers are DOA.
Update: I managed to solve the problem. It was the Realtek Drivers as I suspected. I ended up using DriveSweeper to completely remove the old Realtek drivers. Then I went into safe mode and reinstalled the drivers. Now my speakers work great.
Edited by daveyd, 19 January 2012 - 06:17 PM.