Q: '00 Buick Century Custom. V6 3100. I am at a loss...

to start off, the car died while idling 2 different times. The 1st time I didnt notice right away so the battery drained almost completely. The 2d time I caught it right away nd it started back up immediately but the last time I drove it it almost died when I slowed down 2 round a corner but "came back 2 life" when I gave it gas nd I made it the rest of the way 2 work(another 2 blocks). Omw home from work it overheated (thermostat) so I pulled over nd shut it off. When I tried 2 start it again it acted like the battery wasn't charged enough. hasn't been driven since. If I fully charge the battery nd leave the car sit 4 a few days it'll go dead. My 1st thought was alternator but it doesn't drain while driving or running. i replaced the thermostat, plugs, wires, air filter, fuel filter, and changed the oil last night. going 2 check all fuses/relays and recharge the battery and get it tested today and see what happens from there. if the issue is not fixed what should be my next step?
My car has an automatic transmission.