Intermittent will not start, how to fix this?

A couple weeks ago I drove my vehicle to the gas station a couple blocks away. When I came out of the gas station my vehicle would not start, it just kept clicking. I had a friend come jump me, I had to jump my car every time for the next day. The first thing I did was check all fuses, checked my battery, and my alternator. Once I connected my battery backup it started just fine after those 4 or 5 times. Again, I stop at the gas station, it won't start again. This time it just clicks once. I tried jumping it, nothing happened. I had several men tap on my starter for me while I tried to start it. I let it sit overnight at the gas station, came back the next morning, got under the vehicle myself while a friend turned the key. I got it to start on the first try. It started fine every time for almost 3 weeks. 4 nights ago, I drove home late, went out the next day, it won't start.
It has correct oil in it.
It has antifreeze 50/50.
It has fuel.
The battery is good.
The alternator is good.
The fuses/relays are good.

What should I look at next? Could it be a bad connection at the negative to the battery? It does have some corrosion. I can't get the negative cable back off because it is stripped way bad, any suggestions? If my starter was bad, why would it continue to start without a problem for so long? Also, it does spark at the starter when I knock on it while attempting to start the vehicle.