1. Check Distributor and coil/ignitor -notorious for going bad.
2. Fuel pump and/or filter- make sure engine is getting fuel and not clogged fuel line.
3. Coolant sensor- don't know if it checks temperature or flow rate, but my dad had one go bad on his 88 accord and caused the car not to start. It would crank but not start.
4. Since the guy said it just shut off I would definitely get the timing belt checked. This is an "interference" engine so if the timing belt broke, pistons and valves hit each other and could have caused some internal damage.

Just some ideas, good luck.