Won't start...Battery???

I have an early 90's Lebaron and am having some issues. Early last week it just didn't start. Pushed it out of the garage and it boosted just fine. It ran all week no problem. After sitting all weekend it wouldn't start again this morning...sounds like it it trying to start (not completely dead like last week) but not even close to turning over. I have had the alternator replaced about 6 months ago. Still has an old battery...any diagnosis? I'm guessing bad battery...but I'm no expert.

Any help appreciated...

Thanks,
KAL

More details...I hooked up a battery charger on it last night and the running lights and tail lights came on after some time. I removed the charger and the lights stayed on but eventually went out. Keys were not in the ignition. I still think the battery needs to be replaced...it is pretty old...but is there an electrical problem I need to look into??

KAL

An old battery huh? Well, most parts stores can and will test it for you for free to tell you if your battery is indeed dead (or at least dying) as you suspect. They can tell how much charge it's taking as well as if it'll hold a charge under load.
But until you rule out the battery either way, hard to say if you have another electrical problem or not.

battery basics... batteries have these "plates" thate are pretty close together... if the car hits a bump/dip/jolt of virtually any magnitude, you risk one or more of these plates breaking. when one DOES, you have problesm... sometimes they "short" out on an adjoining plate, and drain the battery. but then we jump the car, and drive it. guess what? that plate can move, and NOT be shorting out... and works OK... til one day it moves again and boom... dead battery.
Get it checked.... walmart has a great battery checker in their shop, lol...

Battery needs replacement