Won't turn over

My brother is repairing for me my mom's old rav. About 90% completed, changed and tuned up everything. I went out and bought a new radio system and he was working on installing it, now the car won't start. My battery is only 2 months old and he says its not dead (he tests it out by flipping on headlights and seeing if they flicker when he tries to start the car).

He has checked all the fuses under the drivers dash and nothing is burnt. He decided to hotwire the car to see if he can get it to crank and it did! But it never starts and It will not crank with the key. He checked the starter it works and it turns over. He's been testing all electrical circuits for 3days now and nothing. All of the lights work on the dash, radio and everything. There is no security symbol light coming on, and no check engine light on. He is stuck. I really want to save money by not going to a mechanic.

Could someone help please

I have been waiting for the guy who bought my beloved 1999 RAV 4 to come get it. Meanwhile, battery went dead. I replaced the battery, started up just fine. Next several times I started it, it was fine. Drove it around a little, then let it sit. We had a bad cold spell, and I did not get out to start it for a few weeks. Well, now it will not start. Tried to jump start, and all I hear is a clicking noise. I can't put much money into it- I just need it to start and run when the guy finally comes to get it this week! I have never had this problem before, until it sat idle for an extended period. Please help.