The "line out" (analog, stereo) is used for connecting to an external amplifer.  Several issues with the connection (1) only use shielded audio cables - do not use "speaker" cables as they are unshielded and (2) keep the connection to 20ft or less.  Also, use a "recording" or "line" or "external input" on the stereo, do not use the "phono" input.

If the hum is not caused by cables or how you are hooking it up, the hum is most likely "ground loop hum" - a difference in the AC ground potential between the PC and the external device (in this case the stereo amp).   Ground loop hum is a common problem in musical amp equipment when two or more AC devices are connected together.  In most cases, removing the ground from one device will cure the ground loop, however, care must be exercised that you always keep the other device and it's ground (shield in the audio cable) connected at all times so you still have the "protected" ground. 

If the stereo amp has a 3 prong AC plug you can use one of the adapters that removes the ground and see if that fixes the ground loop problem (if that is the problem).  Again caution must be exercised as you are removing the "protective" AC ground.  If the stereo only has a two prong AC adapter you can try reversing the AC plug in (if it's not a polarized plug) or again use the adapter and reverse the plug to see if that cures the hum. 

Thanks.  Ground loop hum was the problem.  I bought a ground loop isolator, and that fixed it.

Thanks!