You ain't going to get anywhere without proper battery voltage. It is pointless messing about with a shagged battery and I will wager the fusebox you bought was on eBay because someone had bought a new one to sort there problem out and have now passed it on to you. Sometimes you just can't get away from spending a few £££s. Buy a new battery. Buy a new fusebox. Have the alternator tested. Check to make sure your BECM is going to sleep properly.