Replaced battery and alternator and the battery wont pick up a charge once cables are off. what could be the problem?

There are a couple of fusible links in the car I Think you have a problem with the voltage regulator. Have you tried jumping the car from another car while running if it starts and stays running it could be your starter.Are the cables installed correctly? seen people who have no idea whats going on mess this up try that also did you replace the wires that need to be connectable to the fender some people think it will be just as good but it sounds as if you may have a short.

When was the last time you really did a flush on the system keep in mind do You have a 2 system A/C system if so you may have given yourself a problem the air gets trapped in the core pipes that go back to the rear radiator and a an air log will be there to drive you crazy there is a YouTube video on their auto section be careful don't try flushing when its hot as it will give you 3rd degree burns.