when I started my car it ran briefly, then turned rough and quit on 1994 Honda Accord

The car started extraordinarily quick--then went into a gurgling rough mode and shut down--This took just over a second I would estimate--I then attempted to restart and got the classic monotone whirring like the timing belt is out--timing belt or distributor?? And did I ruin my engine??

4 cylinder 16 valve

2 answers 6 comments
Possibly head cylinder damage internals
take out the top timing cover and inspect your timing belt
And pray it didn't snap
Took top timing belt cover off belt looks ok--distributor has bad bushing-distr. shaft turns a little hard
Timing belt is okay
And you said you inspect distributor
Did you do a compression test on each cylinder?
Didn't do compression test
If the balance shaft timing is off your car would still start but run like shit though
Hows the balance shaft belt?
Turn crankshaft by hand(counter-clockwise) and set to where CRANK pulley is at TDC, then check where cam gear is. Belt may not be broken , it sounds like it is missing a few teeth , though.
My next move then is to line up timing marks and see if the belt skipped?? Will this potentially damage cylinder head?? Even doing it by hand as you recommend??

And what about this thing called the Timing Balancer Belt?? Could that be the problem as it is a belt as well Thanks
Balancer belt is just for that , balancing the engine vibration. Wont affect the running. If the main belt IS stripped , then the damage has most likely already been done , all you're doing now , is confirming it , without complete disassembly.