Starter not working

In november 2011 put in a brand new battery with 750 cranking amps (was told the former battery didn't have enough, I was told this was the solution to the starting problems) it ran for a couple of days no problems, then stopped altogether, been sitting in the garage since november. Now (april)this past week tried to start it, it just clicks, never turns over, friend came over to medium charge the battery, cleaned the terminals, after hours we finally got the car started ran it for an hour, no problems, then took it back, turned it off, and wont start. It just clicks when you turn the key (headlights do work) cant figure out whats truly wrong with it. Search the internet but most all say they start up at some point whether hours or days later.
Car is only worth 1400 at the most and cant afford taking to lexus mechanics or a dealership (both of whom I dont trust) and had problems with them as well. Just don't have the finances to spend. Friend said he would try to fix it, if we can pinpoint the problem.