So much for the easy fixes

It's odd that the 2 units would have different cables if they are the same model though. Are they hardwired or can they be removed? If they can be removed, try swapping them.
If it is the cable, a ferrite ring might help (you know, those things on monitor cables that look like magnets but aren't magnetic

). The only way to know would be to try one. If it already has one, another probably won't help much.
Of course it may be something else altogether. If it's annoying and under warranty, definitely send it back.
RandyT