I suspect the crank position sensor if you are sure that both starter and battery are good. Try to pull the code using the key trick and report back which codes you get.
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01' 4.7 Limited WJ 5" lifted, Rubicon Express 4.5" coil springs with IRO critical path setup and Bilstien 5100 shocks all around, JKS adjustable Trackbar (KOR bushings), JKS HD tie rod (MOOG problem solver Ends), JKS HD drag link (Moog Probel solver Ends), 4.56 Yukon ring and pinion, Moog HD SSD107 Steering Stabilizer, IRO Front drive shaft conversion, Stillen slotted rotors all around with Stillen brake pads, IRO adjustable A-Arm, 3" all the way Kolak Exhaust with High flow Magnaflow Cat. Converter and Flowmaster Super 50 Muffler, 285/70R17 AT Kumho (33") on 17" BlackWheel rims 909B, K&N Cold air intake, Four nozzles Bosch injectors, and Flashpaq 3780.
03' 4.7 H.O WJ 3" lifted, OME HD with 0.5" Coil spacers and Bilstien 5100 shocks all around, JKS adjustable Trackbar (KOR bushings), Moog Problem solver TRE's, IRO Front drive shaft conversion, IRO adjustable A-Arm, High flow magnaflow mini cats, high flow magnaflow cat, Flowmaster Super 44 muffler, 265/65R17 AT Yokohama on 17" Rays rims, and Flashpaq 3780