Do not get fooled into cleaning the air throttle body for built up carbon and dirt. This maintenance on the air input may be needed. but the risk of creating a second problem is a concern, In all cases the electronics will have to relearn the idle and running settings.
In the future to avoid this problem do not depress the gas pedal during battery replacement or during start after battery replacement. Usually the idle air setting is at the right setting after battery change and restart. Depressing the pedal early adds to the relearning requirement. There are solutions that maintain voltage in the car during battery replacement to avoid this inconvenience. The video above shows an 8 mile learning process.
The following link is an excellent explanation of the problem
Well, an engine needs 3 things to run....fuel, spark, and compression. But they also have to happen in the right time in the right amounts. If you are sure that you have fuel getting into the engine, and you are sure that you have spark at the plugs. I think I would be checking the timing and the compression. And remember, just because you have fuel pressure at the fuel rail doesn't nesissarily mean that the injectors are opening.