The burning smell is interesting... I wouldn't expect a busted timing belt to do that. Not saying you can rule out the belt, but I'm thinking electrical. You can check the fuses easily enough, but I'd also take a look at the fusible links (little loops of wire coming off the positive battery terminal). If something shorted elsewhere, those might be blown, and I'm sure that would cause problems.
Check for spark as well (pull a plug wire, hold it next to the intake while somebody tries to start it, see if you get sparks). If not, you can narrow your search down to the ignition.
How low was it on gas when it died? Mine crapped out about a month ago because I ran it low on gas, and it sucked some gunk from the tank into the fuel pump. There was fuel in the system, but it couldn't push it through fast enough. Pulling the pump out and cleaning it solved the problem. It stumbled for a few miles before it died, though... yours sounds more out-of-the-blue.
From what I've read, an engine with a busted timing belt sounds different when you try to start it. (There's no compression since the valves aren't opening and closing.) You say it's still trying to start, so that could be a good sign. Also... if you held the starter for too long, there's a chance that the burning smell came from in there.
Hopefully something here helps.