A better cable may help, but if the hum is that bad then the first thing you should try is re-routing the cables. Especially if the same cables were ok in your old place.

What you really want to avoid is AV cables running close and parallel to power cables. You probably want to try and trace nearby power cables in order to do this. If you AV cables need to cross the power cable, then cross at 90 degrees.

You could also try dropping a small fortune at www.bettercables.com, but there's no guarrantee that this will fix anything. Better to find the disease than treat the symptoms.

<edit> ..or as Tony pointed out, it could be a ground loop. </edit>