Engine wont start, but cranks?

Ok I have a 96 honda civic dx with the 1.6 sohc/non-vtec. I understand you need compression, fuel, and spark for your car to run. I was on my way somewhere a few days ago and my car felt like it was hesitating twice(kind of jerking) on the way there. When I got there I turned it off and thought nothing else of it. The next morning I tried to start it and it cranked, but wouldnt turn over and start. So I started looking around the engine bay for anything noticeable and the only thing I saw wrong was my exhaust manifold was split in half. So I took it off(in 2 pieces). I bought an aftermarket header and put it on. Of course the car still wouldnt start. I bought an obd 2 tester and the codes it threw were, 2 misfires and a problem with the catalytic convertor. So I got rid of the cat all together since I had just put a new header on anyway. I did a compression test and it was fine. The engine is still getting fuel at the fuel rail and it is still getting spark. The spark plugs were black from carbon though and were brand new. Earlier a friend helped out and adjusted the timing a few times and tried to start it, but it still wouldnt start even though it sounded like it would. Instead it just backfired loudly and blew out black smoke. I also changed the fuel filter(forgot to mention that). I have spoken to a few friends that are mechanics and the only thing anybody has guessed is a sensor or possibly the injectors even though that doesnt make sense to me. Well I guess thats all I can say so any help would be greatly appreciated. Thanks