A friend of mine just had a similar issue on a 2005 Tahoe. The heated seats were working intermittently and sometimes turning on randomly. He ended up replacing the control module in the door and it fixed his problem, although I don't know how to "check" for that fix...
In your situation, since it seems the failure is more complete, I'd say fuse first, then maybe the control module. IIRC, his ran him about $300 online.
[This message has been edited by AgEng06 (edited 12/2/2013 3:15p).]