engine will not crank

the engine will not crank. battery, starter, alternator tested and all good. no clicking. i
have tried to start it by giggling the gear shift in D and N. no luck. when i place the
gearshift in any other position it hum's. about 10 starts ago, it seemed that the engine
was struggling to start. it continued to get worst until it quit starting. i have had the
battery disconnected for more than 24 hours. additionally, while the car was running
the lights seemed to pulsated very quickly.this is a 2000 Mitsubishi galant GTZ 3.0 v6.