What you just described will happen exactly when you have a loose ground cable. It's happened to me many times. It draws enough power from the small amount of contact it has to power dash lights, but when it comes time to hit the starter it simply doesn't have a way to pull the power it needs. You'll get a click, and then you'll get nothing until you establish a connection again.

Next time it happens shake the ground cable and see what you get. Don't focus on the battery terminal if it's tight, check the other end.