battery shuts down on start up

I’m assuming it’s a Macbook of some kind since you mention it’s got a battery… year and model would be helpful. Other than that, I think you said your MacBook has a couple of problems:

1. Makes 3 beeping sounds when you start it
2. Does not fully start up and shuts down when the progress bar is around 75%, even after a PRAM reset
3. Only starts with power adapter plugged in, but will run on battery alone after it has started

For #1 - either bad or loose RAM. Try reseating or replacing it. I would unplug the battery before doing this.

For #2 - could be a bad drive or OSX errors - what version are you running? If you have a newer version, get into recovery mode (hold Command + R keys after starting) and try Disk Utility to fix any errors. For older OSX, you’ll need a bootable OSX on CD or USB.

For #3 - you might have a bad battery - common if it’s more than 5 years old.