Magic Trackpad no longer connects

Last week my battery was getting low on my Magic Trackpad (connected to an 2007 iMac). Eventually it stopped working, and I assumed the batteries were dead. So I charged them and replaced them. But the trackpad isn't working anymore.

I know the batteries are charged, because I bought the Apple's rechargeable batteries, and the light turned green after a couple hours to say that they are charged.

I've pressed the power button, held the power button down, restarted the computer, and nothing will get the trackpad to work.

My bluetooth mouse works without any problems.

When I go into the advanced bluetooth settings, I can see my associated bluetooth devices. It will show the trackpad to be off. When I press the power button, it briefly displays it as connected/on, but I don't get any functionality out of the pad. But after about 10 seconds, it switches back to off.

I try discovering it as a new device, but it bluetooth menu doesn't see it.

I think I'm going to try and install it on a different mac (Mac Mini) later tonight to see if it is a hardware or software issue.

Any other recommendations?