Was pulling out of parking lot and every light on dash went on. Tested battery and it needed replaced. Purchased new Battery and drove car all day running errands. New battery drained and all dash lights came on again. Removed Alternator and it tested out perfect. Baffled about what the problem is.
Welcome to the site.
As gray06gt stated, with the key off check the current draw with a clamp style amp meter, or current clamp in conjunction with a compatible meter rated for measuring D.C. current. An AC current device will not work. A DVM can be used. However most DVM's are rated only to measure up to 10 amps without the addition of a current clamp measuring device.
There will be less than one amp current draw for a period of time just after the car is turned off. Assuming all lights are off and doors are closed, etc. That current less than 1 amp if I recall is part of the memory relay circuit. It will drop out after a period of time (don't know exactly that value).
If current is present say 1 amp or greater, look on the battery for a rating called Ah (amphours) NOT COLD CRANKING AMPS OR CRANKING AMPS. THAT IS DIFFERENT. Take the Ah rating and divide in by the current value you read on the meter. That will tell you how long the battery is taking to drain down. E.G. Battery Ah = 72. You read 8 amps of current draw on the battery with your amp meter. 72/8=9. Therefore on a fully charged battery uit will be rendered useless of ALL current in 9 hours. It will likely be unable to crank the car in much less but will give you basic lights and so forth.
If there is no current draw on the battery with keyoff. You have two obvious culprits. Either the alternator is crap, OR you got a crappy battery to begin with. I had that happen with Advanced auto parts batteries. I highly suggest staying with a Motorcraft battery or within the family of the Motorcraft battery MFGR.
If a current drain remains present all you can then do is begin pulling fuses until you find the system causing the current drain. I'd start with the radio since it has been known to cause issues as mentioned. If other electrical mods have been added to the car recently such as a Boost-a-pump, stereo upgrades, fancy neon lighting, etc., remove those sources first to see if the current drain goes away. Good luck.