2005 Jeep Liberty Renegade randomly won't start.

Alright so, I have had a friend of mine who is a mechanic look under the hood of my 2005 Jeep Liberty Renegade 3.7L and he "fixed" the problem for temporary use. The problem I am having is that sometimes my car refuses to turn on when I turn the key. There's no click, there no revving, no sound at all. Most of the time it actually turns on and there no problem once its running. Now, he did rule out a lot of things. He tested the starter, and it works no problem. He tested the battery and the alternator, no problems there. My battery is also brand new. Then he tested the Starter relay in the fuse box under the hood and found there was no power being read on his testing machine (don't know the name of it). He told me I might have a melted or shorted wire that goes to the starter relay and that I would have to get the wires replaced or fixed for a permanent solution. What he did do was splice the wire that goes to the windshield wiper relay and connected it to the wire that connects to the starter relay. The car turned on with no problem after he fixed it. A day later I went to the grocery store with my family. After we got out I attempted to turn on the car, and the problem came back again. It wouldn't start. After about 45 minutes of fumbling with the relays under the hood because I saw what the problem was, I switched out the starter relay with a random other relay that looked the same, tried starting, and still no response. Then I switched them both back and still nothing. Finally after frustration that I had to call AAA I slapped the fuse box with the lid closed and gave up. I guess I was lucky because I tried starting the car one more time and it turned on and I was able to get home. From there on, sometimes I would start the car and the windshield wipers would turn on once and go back to its resting position. I don't know if this is good for the car.

Anyway, since then I have been worried about going anywhere because I was scared of being stranded far from home. So here I am and my question is, does anybody know of a more permanent solution? I know I most likely have to get the wires or wire that are messed up replaced, or change out all the wires that connect to the fuse box under the hood. The problem is I don't have a way of getting to a mechanic to get an estimate, and I'm worried the fix might be way more than I have at the current moment. Does anybody know how much a fix like this would be worth? Is there another solution? I was thinking perhaps removing the wires from the windshield wiper fluid motor relay that is next to the windshield wiper relay and just connecting those wires to the starter relay considering I can just hand wash my windshield if need be. I don't know if that would cause any problems so I have been holding back on doing anything. I just need the car to work for another year or so until I get enough for another car. Thank you for your time and any knowledge you could bestow upon me.

- Ben