If it cranks and no start, check the cold fuel pressure.

 

Check cold fuel pressure.

 

My H3 would crank over and not start also specially in the morning, I did the whole wait ten min. BS and then it would start so I did this and it worked perfect.

I also had another start issue where I would try and start the car and all the lights would turn on but it would not even crack over at all, I took it to a mechanic and he told me it was the computer he wanted to charge me $1200 to change it out, so I did it myself for $150 bucks but that didn't work, good thing I didn't agree to get that done, so a friend of mine recommended another mechanic and he found the problem, it was the "Start Relay Censor" he charged me $100 bucks(cant beat that) at least start with the start relay sensor its like $12-$15 bucks(the sensor is an OEM omron 5810-0201), now my H3 starts with no problems at all, not sure if that is your problem but good luck.