Charged battery, but doesn't even try to start.

1....Don't get wound up in all the symptoms. Pick one and chase it and often the others will fall in line
2....You MUST have some tools. A service manual. Go over to MyMopar.com and download one. A multimeter, and 12V test lamp, and sump alligator jumper leads
3...Do you have HEADLIGHTS? Are they bright? Leave them on and twist the key. Do they die? Do they stay bright? What exactly happens. Did the starter relay click when you twisted the key? If not, and if the headlamps stay lit, jumper across the two large exposed terminals on the starter relay with a scewdriver. Anything? Cick? Buzz? Anything?
4....Start by removing the battery clamps and inspect and CLEAN. With a battery post cleaner tool.
5...Measure battery voltage at the posts. A fully charged battery is 12.6, will be less if cold. Turn on headlights and re-measure. If it is below 11V the battery is either dead or cold. YOU CAN AND MUST NOT charge a cold, dead battery. If it is below freezing and the battery is dead you really need to bring it in, warm it up and go from there. Dead batteries can freeze, healthy, charged batteries do not

My guess? You may have a charging problem, and might be as simple as a slipping belt, etc, that allowed the battery to "sag" as you drove it and ran it down dead. If the battery is down enough to be "dead" you need a larger charger, at least 6A and better, 8-10A