Did an engine swap from a vech to a non vtech. Engine cranks, turns over, but wont start

There are a couple things.
The ECU is looking for an oil ;pressure signal to let the VTEC solenoid work which will whut down the engine if you don't have it in a "Closed" switch position. So you would need to find this on the harness and twist the 2 wires together. You might have to find a pinout of the ECU, which you might be able to get from RyWires. Com or theswapshop. Com, to figure out what else you need to disconnect or wire together. I think the oil pressure for the TEC solenoid is one of the major issues, but there are several and you don't want to play a gusessing game with your ECU. You might have to get different ECU all together. Again, the 2 aforementioned retailers can help you out with a used one.

Well, the problem is unless you live near a mechanic that does swaps, no one is going to mess with it.
If you really want to make sure it works and everything is easy on you. You should call theswapshop. Com and tell them your situation. You will send them your engine wiring harness and maybe your ECU to get a good deal on another ECU. Then you will have them re-fabricate your harness, get the correct ECU and any adapters you may need and it will all just plug in when you get it back.
You can look for a swap shop near you. The only ones are generally in CA and there is one in Baltimaore, MD. Otherwise you are best to go witht the swapshopguys.

Have you checked what is missing, sparks or fuel?

No, that definitely is not the starter as the starter is for cranking the engine and you don't have any problem with that.

http://www.2carpros.com/articles/car-cranks-but-wont-start

Try above link.