You said you checked the ground and tightened the terminals but did you clean the battery posts and inside of the terminals? If not then tightening will do little to fix the issue. If so it's now time to get a volt meter out or try a battery style jump starter. With the volt meter you can compare voltage at various points like + battery post to frame ground, battery ground post to solenoid etc to narrow down where the voltage drop is when you turn the key. It's also possible that the starter is bad, you can remove it and have an auto parts store test it. If you try a jump start battery and it does the exact same thing I would say it's the starter. You asked where the solenoid is, my guess would be on the starter itself. The dimming lights is what points to bad connection, bad battery or bad starter.