[JPonLKN]

I agree...bad ground. Just because it is tight, doesn't mean its right. Take every ground wire off its mounting point, clean any corrosion down to bare metal and re-assemble. Also, the solenoid plate mounts to the battery tray, which mounts into the frame. As both the tray and frame are painted, and ground is often made at the tray, its a weak ground path back to the frame as it relies on going through bolts at painted steel. Extending a ground from the battery negative terminal to the battery tray or any point where grounds come together is likely to help. Also, make sure the bare heavy gauge ground wire that connects to the block under the coil is in contact with the block, not the plastic shroud.