you said you did a engine swap from an h23a to an h22a, did you do the work or did a shop is my first question? did you or the shop do it correctly because you have to have a few coolant hoses that arent ran in the engine bay of the h23a assembly, like on the h22a engine bay, if in deed everything is where it needs to be for the swap to work, than timing is what im pretty sure it is. If you did the timing yourself or with your friend then my guess is the camshafts or cam gears arent timed properly. The very first time I rebuilt my head on my f22b DOHC, I thought I did my timing perfectly except my skunk2 cam gears weren't as easy as the stock gears "in other words they don't have dummy marks on them that are completely obvious and sure enough I found out my timing was off 90 degrees which when I tried to start the engine made me think the same way you are, I thought it was gas, or spark related because the car cranked and cranked sometimes even backfire but never start. Deffinetly get your timing checked by a respectable honda technician I really think thats what it is. unless like stated at the beginning the direct swap wasn't done correctly. goodluck