I have replaced my battery, but still no power?

Have recently replaced the battery on my 'L' Reg Vauxhall Cavalier as i began to encounter problems with it turning over and stalling at lights etc. I put it down to the winter and having short journeys with heater, wipers, lights etc on full blast. Having replaced the battery, everything was fine for a week or so, but now beginning to have problems with starting the car again. It seems something is draining the battery and not holding its charge?? Can anyone help?? Thank you.