I've had this problem for about a week now, replaced the battery but something is still draining the battery while the car is turned off. The alternator is working fine and I can't find any shorts. Any ideas?

You can check for parasitic drain with a multimeter (DMM) at the battery negative cable and troubleshoot accordingly. The reading will be in amperage - millivolts. It should be well under 40-50 mA but it depends on the reserve capacity of the battery.