If everything checks good, then you need to follow a diagnostic flow chart. I attached all of the directions below. One of the things is suggests first is to check for diagnostic trouble codes. I don't know what kind or if you have a scanner. This will require one that is a bit more complex.
Regardless, do this and let me know what you find or if you have other questions.
Repair Safety Notice: This information is for general instructional purposes only. Vehicle repair can be dangerous. Verify all information, follow manufacturer service procedures, use proper tools and safety equipment, and consult a qualified repair shop when needed.