S14 drawing power when car is off? HELP!

[snow hawk]

Sup fellow zilvians;

I bought this bone stock base model s14 a couple weeks ago. I noticed it had a weak start, and we chalked it up to a battery that was too small. Last night, the battery was dead, so I swapped it with a known good battery, and car started right up, even easier than it had previously. I turned it off, let it sit for a bit while I put tools away, and came back, and weak start again. I drove to a buddies, hung out there for a few hours, and started it up with a weak start again. I came out to my car this morning and the battery is bone dead. I previously noted a beeping when the door was open, and I realized that my key could be pulled out without the ignition being off, but I remedied it by turning the key all the way off and pushing the key release button, and that stopped it, but now the battery is dead. Anyone know where I should start to see what's drawing power? This car is my daily and I really need it to be running... Please help!

Thanks in advance!

V/r
Mike