You might have an ECM or PCM issue. From another forum:
Powertrain Control Module (PCM) or Engine Control Module (ECM) controls the starter relay based on input from the key switch. When the ignition switch is held in the start position for 0.4 seconds, the PCM/ECM start timer is activated. Once the start timer is activated, the PCM/ECM will continue to crank the starter until either the engine starts or a no start time limit is reached.
The other symptoms sound like fuel supply, but if the ECM or PCM is not functioning properly, it could be causing those symptoms also.