What year is your KJ?
Battery light usually means alternator not charging...you need to put a digital voltmeter across the battery.
Should show 12.5 volts with engine OFF.
Should not drop below about 10 volts while cranking.
Should show about 13.4 volts while running.
Misfire could be the fuel injector.
Let us know the above information please then we can give you further advice.
You can download the Jeep KJ Service Manual for your year KJ...except 2004....below.
I cannot find P1682...need to know year of the Jeep but P1684 is "Battery Was Disconnected". Could be related to the Battery light coming ON.
With a meter across the battery while running voltage should be about 13.4 volts.
If not check the Grounding Straps grounding engine to chassis....a strap from the rear of each bank I believe. If 13.4 volts is not at the battery, move the lead to the large lug on the alternator....if 13.4 Volts is there with respect to ground then the thick wire going from the alternator to the positive lug of the battery has blown!
This thick wire is called a Fusable Link ie. it has fuse built inside it that will blow if there is a major short. If blown, a new correct rated Fusable Link has to be fitted.
Early KJs had a Battery Temp. Sensor located under the battery which measures the temp of the battery and gets the PCM to slightly adjust the charging rate.
What the Owner's Manual does not mention is that this temp. sensor can also cause the Charge Light to come on...I had this due to Ground going missing on the one side of the Temp Sensor!
www.colorado4wheel.com/manuals/Jeep/KJ/