Battery over charging

Bought an 01 4.0 auto 151K last week. The battery gauge likes to randomly spike and go back to normal. I go out today (after not starting for a week) and its stone cold dead. Jump it started very slow, let it run for a bit, shut it off, back to stone cold dead.

Do you think its just a bad battery causing the issue or underling electrical problems? I changed the terminals right away cause they were shot so thats good to go. Also have a spare alternator if we think thats the way to go but i doubt.

Begin with basic trouble shooting of the start and charge systems. Remove, clean, and firmly reconnect all the wires and cables to the battery, starter, and alternator. Look for corroded or damaged cables or connectors and replace as needed. Do the same for the grounding wires from the starter to engine block, and from the battery and engine to the Jeep's frame/body. You must remove, scrape, and clean until shiny, the cable/wire ends, and whatever they bolt to. Jeeps do not tolerate low voltage, bad connections, or poor grounds.

The battery and the alternator can be tested at the auto parts store. A failing alternator can over-stress and kill a battery.

Most likely the alternator is bad. If you have another one lying around already then go ahead and put that in.

You will need to do some testing for voltages with a VOM (mulitmeter).
Jump start the Jeep and test the idling voltage at the battery; should be 13.3V+. Could be as much as 14.5V depending upon condition of battery and charging system.
A good battery should be 12.5-12.8V at rest with engine off....
Dirty or loose battery terminals can kill a battery due to intermittant charging by the alternator.