Engine will not crank

What exactly does the starter do when you turn the key? Spin and not engage? Nothing at all? Click? If you turn the lights on and turn the key do they dim? From the description I'm thinking it could be the starter relay or the wiring to the solenoid. A quick way to test would be to pull the starter relay out, then use a jumper wire between the 30 and 87 terminals. If the engine turns over every time, there is an issue in the relay or it's control signal. If it doesn't the problem is in the starter side of the system. To test that take a simple test light and touch the two outer relay contacts in the socket and have someone turn the key. Have them do that in park and neutral. You should be able to narrow it down quick that way. Relay wise, the AC relay is the same so for testing you could swap it into there and see if the relay is failing.

Okay, so the starter locks in, but the engine doesn't turn, and you can easily turn it over by hand? If yes, take a meter, connect it across the battery, and see what the voltage is, then engage the starter and see what it says. If the voltage is good at say 12.6-12.8 and engaging the starter doesn't drop the voltage at all, or only very little you have a bad battery connection or cable. To test which cable is the problem, take the meter and connect it from the battery negative to a clean spot on the engine block, you want to see very slight voltage like.005 volts or less. Turn the key, does the voltage stay at that very low level? Now do the same on the positive cable using the battery terminal and the battery post on the starter solenoid. Does it read the very low voltage and stay there? I'm thinking that one of those cables is going to show well over a full 2 or three volts, if one does, first clean the ends very well, and test again, if you still see the sane numbers the cable has failed internally. Replace it. For a faster test or if you don't have a meter handy, connect a set of jumper cables up in parallel to the battery cables, so one from battery negative to a good ground, try to start it, then from battery positive to the starter's battery feed terminal.
If you have the meter on the battery posts and do see it drop a lot when you turn the key, but still have no starter action you have a bad battery. To verify that you could try jumping the vehicle with another one or pull the battery and take it to be tested. I have seen brand new ones fail a load test due to internal damage.

Both relays are the same so if it worked, they are both okay, it still sounds like corrosion though. Fairly common in the Libby's. If swapping the relay helped though it could be worse and actually be corrosion in the fuse center. That happens as well, the rails corrode and cause the same problems. For that the only way to tell is very close examination, pull the relay and look into the connector slots, you are looking for fuzzy green growth, if you see any then it's likely there is a lot more as the contacts are usually the last to corrode.
But I would also check the voltages at the cables to rule out issues there first.