The intakes are most probably NOT the problem - removing them would be a waste of time.
My guess is that the battery is shot.
First thing I'd do is put a VOM across the battery terminals and check the voltage - should be around 12 and a half volts if the battery is in decent shape. Then measure the voltage across the battery terminals when you can get the engine started. If voltage climbs to 14 VDC or so, the battery is probably bad. If volts stay the same or drop, the alternator/charging circuit has a problem.
Most auto parts stores will test your battery for free.
The FSM will have diagnostic procedures.
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