I don't have an answer to this as I'm looking for information myself on how to change the battery in my Tom Tom 720; perhaps for the same reason.
I only wanted to comment that I, too, have smelled a very strong burning smell (although no visible smoke) coming from my Tom Tom when it was plugged into the cigarette lighter and I, too, have wondered if that is why my Tom Tom won't work.
This is sounding like a flaw of some sort with these devices which I now think needs to be brought to the attention of Tom Tom.
VeniceParrish, April 2010