Sounds like you've got a bad electrical connection somewhere, probably in the battery terminal end or where the ground ties into the frame. Once you've cleaned and re tightened them, try shorting across the solenoid with a screwdriver. If it cranks that way, then you've got some kind of problem between the switch and the solenoid.
Have power, everything lights up when switch is turned on, just no turning over, not even a clicking sound. I guess replacing the switch would be the least expensive to try. Ground off battery is tight, all connections to solenoid are tight.