Any help would be appreciated:

I think I've got the cradle issue worked out, at least temporarily. But here is what is still going on with the remote itself:

I put it to charge and it doesn't beep, it goes through the reboot process, I can see the slideshow kicking in, I see the battery indicator as all red with a question mark through the middle of it and after a while the screen goes black. I let it be there in the cradle overnight and this morning, no charge.

Any thoughts?