The green key light only comes on after I try and start the car and cut the switch off. I have power the the battery 13.5 amps. But still no starter engagement. I need some help with the diagnosis. The only way to get it running is to bump start it.

 

Is the green key light flashing?
Battery terminals tight and clean?
Fuses good?
Good ground to engine and power to starter?
Good signal wire to starter?
I sure hope your battery isn't producing 13.5 amps. Thats nowhere near enough for your starter. I'm sure you meant volts

When you say bump start do you mean roll start? Roll it and dump the clutch in gear key on? Or do you mean crank it with jumper cables hooked up?