Sounds to me like you MAY have multiple problems.
First, check your belt for tightness and glazing/cracking (Jeep IS 11 years old) which would allow your alternator to not output correctly at lower speeds (may be why it continues to run at higher speeds) and allow battery to discharge with time.
Second, as mentioned in previous post, disconnect Battery Post Clamps and clean them until "shiny bright".....do not forget to do the same to the INSIDES of the clamps. This corrosion spot could have prevented your battery charger/alternator from charging your battery. Also, a discharged battery can take HOURS to recharge, depending on the amperage of your charger.
Third, make sure clamps are re-installed on posts and CANNOT be wiggled by hand after tightening.
Fourth, IF you can get vehicle running, measure across battery terminals with a voltmeter (or observe your dash voltmeter). Should be greater than 12.5 volts. This could be as high as 15 volts and should not drop below 12.5 volts with ANY and all accessories (lights, heater, blinkers, etc.) turned on.
"For Gawd's sake, put a RELAY in there or you could burn the whole damn Jeep to the ground" ...this quote brought to you by people who do not understand the law.....Kirchoff's, Ohm's, or Faraday's.
Violation of KISS shall always ring false in TRUE engineering. - ME___
Had 75CJ5, 89YJ, 93YJ. Have 82CJ7 & 95YJ____Not one burnt yet due to lack of relays.