Your 96 Honda Accord would not start the mechanics informed your that your timing belt needs to be replaced what is the probability that there was engine damage?
If the engine was running and suddenly stopped of its own accord (excuse the pun), especially if accompanied by noise from engine, it is almost certain that the engine has been seriously damaged i.e. is the mechanic saying that the timing belt has broken or that you should have it replaced before it breaks?
If the mechanic's comment was made as an observation after curing the original failure to start - have the belt changed before you drive any further.
The Honda literature states that the 4 cylinder is an 'interference' engine, meaning damage was done to the valves if the belt broke. But there is plenty of info online that it is not actually an interference engine, and I'm familiar with at least two cars that broke belts that did not damage the valves at all.