There’s an electric fuel pump in the fuel tank on that car.
Underneath the back seat you can find an access hatch (a round cover with three screws). Every time you turn the key on, you should hear a buzzing noise from there for a few seconds. Another way to check is by disconnecting the fuel supply line and running it into a jar. It’s the line that comes from the center of the fuel filter. If no fuel comes out of that line when you turn the key on, then you have a problem with that pump. Could be just a fuse, #28, or the pump itself. Some cars will run without that pump, some will not, and it can depend on how much fuel is in the tank.
To check the timing belt, you need to turn the engine so you can inspect the entire length of it for missing teeth. They like to strip teeth, and at a glance the belt still seems fine, until you find the affected section.
It’s also possible for the cam sprocket to slip on the cam hub, throwing the cam timing out so the engine won’t run. It’s held on by three bolts in slotted holes. If it slips, the bolts will be all the way to the end of the slots. They should be near the middle. This would happen if they are not torqued to the correct spec after a timing belt job. The result is the engine just stops dead, and it won’t start until the cam timing is adjusted back to spec.
I have never heard of a tandem pump actually failing. I think they wear until they start leaking, and at that point should be replaced before they actually fail. Also it would slowly get worse and worse, and probably wouldn’t just stop unexpectedly in the middle of the road.
