If like you said its a JDM loom, and its only the Engine loom, not the entire car loom aswell, you may be missing a relay for the injectors. This is what you need to do to check.
Go to your ECU. Check that the BF pinout on the 10pin plug to the LEFT.
Check that this has 12v when the key is turned to ON (Ign ON). If it doesn't, temporarly add a wire from BF to B+. Try to start the car again and see what happens.
Ecu pinouts below.
Also, I find the best way to check if your spark is good is spray start your bastard into the throttle and then try and start it, if your timing is out it could back fire, if it isn't it will run breifly.
Try these 2 things and let us know.