Weird starting problem

Hello everyone...I am new, and I did a forum topic search to see if anyone had a similar problem. I did not find one, so if this has been a recurring problem, I apologize in advance. Some boards hate new posters and I understand that. I have been walking now for over 7 weeks. That is the last time my Jeep started. This has been a very frustrating problem. I do not have alot of time to work on it because of work and stuff...

Vehicle Description:
95 YJ
2.5L - 136,000 miles

Problem: The YJ will not turn over. I turn the key and here a very short hum and then a single tick at the starter relay (fuse block by the battery). Everytime I turn the key over, it will tick once.

This problem started out of nowhere. It was starting fine and then BAM! I noticed the terminals were corroded the first time, so I cleaned them up with some Coca-Cola and it started right up. It started fine six times after that and then died again. This time, I had to smack the starter a couple of times (but I also wiggled wires around), and it started right up. It started four more times, and now it is dead...It acts like it is not drawing enough power to engage the starter...

This is what I have done so far:
1. Had the battery tested at Advance Auto on a load tester - reads as having full charge.

2. Had the starter tested at Advance Auto...they said it was fine

3. Tested the starter relay...it is fine

4. Cleaned the terminals and all connections...they are fine

5. Tested the power source with a continuity tester...I have power from the battery to the starter...The + wire on the starter has power when the key turns over...(I did not test with a voltage meter though)...There is also power from the battery to the fuse box...The headlights and wipers work (headlights are really bright)...

6. Engine is not locked up...

I have ruled out the ignition switch because I get the click at the relay...Any suggestions would be greatly appreciated...I have to walk four miles a day to work, and that is not a joke...I am too stubborn to call a tow truck...

I would start by replacing the positive cable to the starter and fuse box. It's likely that the inside of the wire is corroded. Is your jeep and Auto? Why not pop start it to get to work, just remember to park on a hill. :-) Keep us posted

I would start by replacing the positive cable to the starter and fuse box. It's likely that the inside of the wire is corroded. Is your jeep and Auto? Why not pop start it to get to work, just remember to park on a hill. :-) Keep us posted

Haha...I wish it would have died on a hill. It is in a flat location now behind my apartment complex. Last night, my buddy and I tried to push start it, but we didn't have enough room...It was something to see though!

I tested the power with a continuity tester from the battery to the fuse box and the fuse box to the starter. It shows that the wires are hot, but I haven't checked them with a volt meter yet...

This has been the darndest thing I have ever experienced! Thanks for your reply...Tonight, I am taking off the battery cables and replacing them...at this point, I am really desperate...

LOL. This summer I was at the bar watching baseball and I my battery was definately near death, so when I came out the damn thing would not kick over. I pushed it by myself (no doors or top) and then jumped in it while rolling backwards and popped the clutch. Had to be funny to watch. Also, you might have an issue with the ground wire to the engine. Make sure all cables are free of corrosion.

Well, as weird as this may sound...It worked itself out...I took off the battery cables, cleaned every single ground/contact...I also took the starter off and fooled around with it for awhile...

If I had to guess my problem...I think it is related directly to the starter solenoid...I made a couple of strategically placed shots with a hammer to the necessary areas of the starter, and a few wire jiggles!...