So, here's what's going on:

It's a 2002 KJ 3.7 with 190,000+ miles. About a year or so, maybe less, had a problem with stalling at stoplights and had the throttle position sensor and battery replaced. Less than a month ago, the battery light came on, eventually determined to be a bad alternator. Replaced alternator, has run fine with the new one. Still have the year-old battery in there.

Then Saturday I drove it 50 miles to work and it ran beautifully on the trip in. It sat in the parking garage there for 8.5 hours, after which it started up and immediately stalled. Popped the hood, no obvious issues. Belt was good, nothing oozing or smoking. Tried two more times to start it and as soon as I let the rpms drop back to idle it stalled. On the next try, finally ran without stalling. At this point it's again running beautifully, no misfires, smooth and steady. Drove it home with A/C and lights on, no dimming at stoplights. The next day it started fine at home and work, no issues. Stopped for gas near my house on the way home and it started again but reluctantly. Stopped and restarted it again when I got home (maybe 2 miles, if that) and it started strong again. This afternoon at home after sitting overnight, same situation as Saturday: Cranks over and fires up, dies as soon as I take my foot off the gas.

None of the idiot lights are on. I've been too busy to investigate it yet. I basically do nothing but work, watch my 4-year-old daughter and sleep until my weekend comes (Weds/Thursday). If I can get to a parts store I'll see if they can pull any codes. Ordinarily from the symptoms, I'd be thinking TPS again or the battery is on its way out. But I'm perplexed by the fact that sometimes it runs fine. It's been a long time since the plugs were changed, and I'll check them when I can. But aside from my theories, anyone have any ideas/advice?

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2002 KJ (un)Limited 4x4: OME HD lift, ARB bullbar, Warn 4X flood lights, Skid Row tranny skid, Mopar engine, transfer case and fuel tank skids, Boulder Bars, 245/75/16 Goodyear Duratracs on Moab wheels.

'stalls on start' sounds like a Sentry Key Sytem malfunction. The thing has an interuppter that prevents the engine from running.

edit: to elaborate, my TJ did this for a while. I cleaned the key extra carefully and solved the problem. But the SKS chip can malfunction, and seems able to waffle in and out. A dealership can check your key for you to make sure it's not damaged.

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07 Liberty Sport, 245x70r16 Goodyear Silent Armor
02 Wrangler Sahara, 31x10.5r15 Goodyear Silent Armor, ARB Bumper, Patriot Rear Bumper w/tire swing

do a load test on the battery, sounds like a battery condition to me

If the sentry key is bad then a little key will light up on the dash when it dies after starting it.

If it cranks good then its not the battery. Check the terminals just to be sure.

If it idles nice and smooth I wouldnt think the plugs would be old or the engine would be dirty.

Check the codes just to be sure.

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LOST KJ'S
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Current Jeep: 2004 Jeep Liberty
-Atlantic Blue
-Air Ride Rear Suspension ; OME/Rustys Lift ; Powertrax Locker ; Moog Lower Ball-Joints ; 245/70/16 Yokohama Geolander A/T-S's on MOABS ; Flowmaster 50 SUV
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What gas brand you usually use. I like to run a top tier gas such as Shell. Might have carbon buildup around the valves. Try running seafoam through the vacuum into the intake and mix into the oil. Change the oil after 30 minutes of driving and change the plugs.

What about the timing chains? Might that be a possible cause?

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2002 Jeep KJ Sport 3.7L 4x4

245/75-16 Mastercraft Courser HSX, 16x7 Cragar, 2" OME MD Lift, ARB Bumper
AEM Brute Force Cold Air Intake, Flowmaster Super 44 Muffler

Currently working on: Full service on transmission & bed-lining ARB bumper

viewtopic.php?f=43&t=84650

Check the batter as sprsonic suggested

What happens at times is when an alternator goes it can fry the battery with it, not always but have seen it more times than not.

Thats where I would start

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MUDD'S MOTORSPORT'S We do IFS lift installs ,
03 OVERLAND EDITION /Kilby-Skidrow-Mopar-4XGuard skids/ 2.5 inch TOTAL CONTROL JBA coilovers -JBA Arms/MOABS-31 FALKEN WILDPEAK AT3W / 4.10's etc, 04 Kilimanjaro Edition loaded, plus 05 KJ limited

Thanks for all the replies! Yeah, Tom, I was kind of surprised that the battery wasn't shot when the alternator went out. I'm gonna start there anyway, but I think it's OK still.

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2002 KJ (un)Limited 4x4: OME HD lift, ARB bullbar, Warn 4X flood lights, Skid Row tranny skid, Mopar engine, transfer case and fuel tank skids, Boulder Bars, 245/75/16 Goodyear Duratracs on Moab wheels.

So, finally had time to deal with this. Turns out almost everybody was right. Battery was marginal, throttle body gunked up, spark plugs toast. Runs like a dream now. I'm usually really diligent about maintenance (don't get to 190K otherwise), but lately my life's been running me instead of the other way around. Back to work tomorrow. Thanks again for the suggestions.