Renult megane scenic won't start?

Hi, can any of u guys help me out please? My megane scenic 2006 reg will not start. This started happening when we had shut the engine off one day but still sat in the car for an hour, and when I went to start it the battery was dead. I got someone to help me jump start it and then it worked fine. This happened on a number of occasions and after a jump start it always worked fine from then on, until the other day when I were driving it and all of a sudden a red light saying STOP shown up on the dash, and it were also showing up as battery low. After another mile or so there were all kinds of warnings showing up like handbrake failing and no power steering etc, and I could feel the steering very hard to turn and as I pulled down a road the car packed in on me and wouldn't start again. Anyway I got the AA out and they just hooked a battery booster up to my battery and it fired up straight away, he tested the altinator and the battery and said both worked fine and both read the correct voltage etc, and he couldn't find anything else wrong with the car. He did say that the red cap is missing that goes onto the positive side of the battery and the connections could do with a clean with a wire brush or sandpaper though. I drove the car home with no problems, and the same night I nipped to the shop and exactly the same thing happened again, it conked out on me and wouldn't start. I looked under the bonnet and saw the connections that went to the red plastic tray bit, and I touched one of the wires that were connected to it and it snapped off. Also I looked at another wire that went to the same plastic tray but to the opposite side of the wire I had just snapped, and I could see it bulging with a dirty powdery substance so I twiddled the wire either side of where the powder were and it all fell out, leaving a big gap where the copper wire should be connected. It were like the copper wire had turned into this powder because it had still been working whilst it were there, but now I had got it all out it left a gap so the one wire weren't joined together. I tried to get a little piece of wire just to attach it where the gap were and it sparked a couple of times then were dead. That's it I were locked out and had to get a recovery truck to tow it back home, the guy who cam tried a few things and tried it with a booster pack but there were no life whatsoever. The next day I took all the wires off the battery and cleaned them all, rewired the ones that had snapped off and been damaged, and put them all back together. The battery were still totally dead so I hooked up my battery booster I had bought and straight away my car started, I revved it a couple of times and it idled perfectly so I took the negative clip off the battery from my battery booster and the car then cut out, so I tried it again. It fired up again but this time a warning came up saying battery low, I left the booster on a little longer but still when I took it off the car shut down. I didn't want to leave the booster on the car whilst running too long incase it broke it so now I'm at a loss and don't know what to do. The guy from the AA tested the battery and the altinator and said both were perfect so I am seriously at a loss and can't afford to get ripped off at a garage as most do not understand anything about renults, can someone please help me? Thanks in advance