1995 f250 351 just clicks but only does it randomly

My 1995 f250 with a 351 started having issues
with just clicking when you would try and start it.
So first off I replaced the battery since my old one
was about ten years old the new battery has
850cca. That didn't solve the problem so I replaced
the starter with a brand new not remanufactured
one still same problem. So next I replaced the
solenoid on the fender well and  it started so I
thought problem was fixed.next morning it started
clicking again so I rechecked everything and found
my battery cables to be pretty badly corroded so I
replaced them also. Truck has been fine for about
a month and now has started giving me the same
problems again. It might start every time for a
week then next time click about 20 times before it
will start I'm just confused