the two lights mean that it has overheated and it turns everything off.
The towel trick is not going to do much except let you play your xbox for a couple of hours before it happens again, as well as damage parts that weren't damaged before. Either do an xclamp repair, or take your chances by sending it to M$ and hope it is RROD when they test it.
The towel trick is just a trick, it is not a very good method for repair.