Sanger

Two days ago I was pulling my car into the garage, and turned off the ignition. Everything went off, but usually the stereo will keep playing until I open the door; it went off to. Seems the battery just died. I couldn't open the hatch of doors with the remote and the interior lights wouldn't come on. Today I got a new battery and installed it. I fully charged it before installing. When I went to start the car, it started up just fine, but I noticed the idle came down quick and it wanted to die. So I revved it a few times to get some fuel going warm the motor a lil. After letting off, it wanted to die again. I shut the car off. I tried starting it one more time, and I let it idle. It idled around 600rpm... usually idles 800rpm when warm. I opened to hood to listen closer to the motor, and 30 secs later it killed. Can this be any related to the battery?? or does this sound like another issue. Car was running fine till the time I parked it in the garage and the power all just went out.