I thought I would share my current experience with this problem and I what I've discovered.
I have the aluminum wireless keyboard. I believe I've had it more than a year. Just recently I was getting a low battery warning, although I didn't think the batteries were that old. However, I put some fresh rechargeable batteries in. It worked at first, but very quickly I got the low battery indicator again and then the keyboard would no longer turn on. Considering I would need to buy a new keyboard I decided to try a few things. I tried the tinfoil and paper clip tricks mentioned, but neither worked. I decided to remove the plastic door that was on the underside of the keyboard (maybe that voids the warranty, so be careful!!) When I looked inside I noticed one of the wires had a bare spot where you could see the wiring under the plastic! That could cause a short and drain the batteries. So I put the newly charged batteries and tried them in my digital camera and, sure enough, they were dead!! So now I was sure there was a short in the keyboard. I tried pushing the wire with the bare spot to a place it wouldn't touch anything and put more new batteries inside. Now the keyboard is working again! However, I don't know if that's the only short, or if the wiring will move around again when I'm using it.
Anyways, I thought possibly this might help someone.
DB