Fuel pump failure is the most likely cause but it can be other things. Check to see if the fuel pump is running. Can be a blown fuel pump fuse or bad fuel pump relay. But on a 19 year old car the pump very well may be defective.
Ignition switch
Remove the muffler
Have your alternator checked
Diagnosis: Engine Won't Start or RunCheck related link below
A continuous thumping noise and floor shaking while driving on a 2000 Honda Accord could mean a loose exhaust system. It could also mean a bent frame or a broken spring.
Dirty fuel filter or air filter.
Why does my car die out when I turn on a/c
Check the 1989 Honda Accords timing. If the engine has jumped time then the engine will buck and sputter.
check to see if your car has had the ignition switch recall completed
Bad connection somewhere? Loss of power? (check and wiggle fuse)
check your main relay, that is a problem in those years after a while..
bent wheels or a broken cord in a tire or a deformity in a tire.