Hi, my 1999 Honda Civic refuses to start.

When I turn the key, there's a beeping sound and nothing else happens. No turn over, no nothing. I replaced the battery a few days ago b/c it wouldn't start, and it started up just fine - but then today, nothing, not even on this new battery.
I'm a complete automotive idiot, I barely know anything about cars (heck, I was proud to have changed my battery on my own for the first time >.<) so I am not sure what the problem is. It seems like a battery issue, but this is a brand new, used for 5 minutes battery, how could it be dead?
Any help is -greatly- appreciated. Thanks.