(1999) Honda Civic LX has no power

Greetings Cargurus!

              I am having some difficulties diagnosing the problem with my 1999 Honda Civic LX. For a month or so, I was having difficulties with an old battery so I replaced it with a brand new one of the exact same specifications.

              3 days later, the car simply does not start anymore. I have no idea if the extreme heat as of late in my area had anything to do with it, but there is no power at all when I turn the key now. The lights do not work, there are no sounds whatsoever as I turn the ignition and the only electronic equipment I can get to do anything is the beeping sound when you first put the keys in the ignition.Other than the "beebeebeebeep", its completely dead.

                 I have been considering if it could be the battery cables, the ignition lock, a blown fuse or any of the other electric-related parts (alternator, fuse relay, etc) but am unsure where to start. I have successfully jump-started the car several times to test it, but when I turn it off, it immediately returns to the "nothing-happening" mode.

                 My next step is to check every fuse related to the ignition system and fuel pump, but if its not a fuse, what else could cause this loss of any power or response from the vehicle? I just want to make sure I properly diagnose the problem so I don't go blindly buying every part of the assembly trying to find the right one.