this sounds like an aftermarket alarm, most likely a cheap one or a really old model which you will find hard to buy a new remote for either case. the black push button on the kick panel below is most likely the valet button but you need to know the button combo for it to work.
start by pulling the paneling off and looking for the alarm brain, look for serial numbers and names then look for a matching remote and programming instructions. every honda in junyard that i have looked at with alarms they have all been no name brands so i would advise buying a new one if this is the case for you.