You might have lights but it could be some heavy gauge wiring from the battery terminal that is somewhat loose but not loose enough (that's why you got lights).
Trace those heavy gauge wires from the battery terminal and make sure they are tight. Check the ground wires are well. I have that happen on my car with a little bit loose wire not enough to crank but enough for the lights to come on.
You might want to try to start engine in Neurtal.
Also, you might want to by-pass the starter solenoid and directly connect the starter to the battery and see if the starter would even turn the engine.