car wouldn't start, and after a jump and driving it home, would not start again.

I would check battery cables they may be loose and check ground cable to body and engine for contact. Recheck battery too.

ther is either a draw on the battery or the battery has a bad cell test battery again then go from there. you can check for a draw by putting a test light on post and connecter if the light comes on there is a draw pull fuses untill the light goes ou then that is the problem area

Definitely check the cable connections at the battery. If the battery is only 1 month old, odds are it should have been charged sufficiently from the drive home to restart the vehicle, although allowing the vehicles battery to be charged by the alternator is never a good idea (this will overwork the alternator and possibly cause overheating resulting in reduced operational life of the alternator). Initially there may have been a load left on or parasitic drain somewhere else causing the initial no start, but again, after getting the vehicle up and running, the alternator should have been in good enough shape to operate the vehicles electronics normally, not under reduced power like you are describing. Please keep us informed as to your findings.