Hum issue

I have a basic 2.1 system in our family room I cobbled together from gear I've acquired over the past 30 years or so (just added a used SVS SB2000 sub, which is great).  Everything works fine and such a huge leap in enjoyment over TV speakers -- duh-- but I occasionally get a loud hum through the front speakers.  At first I thought it was it was a bad connection or cable, but I noticed that when I move the HDMI cable a little the hum completely disappears.  Yes, I have the common nightmare of cables jumbled together behind a cabinet that's hard to access, so I freely admit this is most likely a self-inflicted wound.  But I'd like to minimize my time moving cables around in a physically awkward situation, so what's my easiest and best move alleviate the problem?  My instinct is to completely disconnect the HDMI cable and route it so it's got minimal contact with other wires.  Do you think this is likely to solve it, or are there other connections that could more likely be causing this problem that I should focus on first?  Or maybe replace HDMI cable?  Ugh. 

Thanks for any thoughts/help!