1992 jeep yj will not turn over

First check if the switch has power to it: turn key to on, do the warning lights and gauges turn on, and all accessories work?
If so, next check would be the start circuit. If you have a voltmeter or test light, check if the starter solenoid wire has power when key is held in crank. Power there and the starter or solenoid needs testing- it is probably bad. If no testing equipment, take the starter off and have it tested.

You should have a switch on the clutch pedal under the dash. easy to test,,,just jump across it and see if it starts (only with trans in neutral and your foot on the clutch because it can start in gear when jumped) You also have a relay in the power distribution center and a fuse as well. Relay test is simple...most of the relays are the same so just swap positions. You should also check to make sure power is getting to the starter...12v at main connection and 12v at the small connection with the key turned to the start position (again in neutral and at least have the brake on) If you have power at the starter, likely it has failed. Don't forget...ignition switch needs to be working as well.

With a test light follow the wires from the battery to the fuse box to see where you lost the connection. You may have a burnt fusable link. . Run 12 v directly the the fuse box and see if that helps.

you have an ignition voltage problem or ignition box failure.

make sure ground wire is properly routed and the starter cable from battery to starter is in good shape and not all corroaded if the battery is good then the problem is in the cables or starter

Before blaming the starter make sure the battery is fully charged. It should be around 13V.
Starter circuits for the most part operates in the following way. Turning the ignition key supplies power to a relay situated in the engine compartment which in turn activates the solenoid on the starter which powers the starter itself.
Make sure your vehicle is in Neutral(Manual gearbox) or Park(Auto box) Locate the starter motor. On the starter there is another cylinder like object called the solenoid. There is a thick red wire running from the battery connected to this. There is also a much thinner wire which activates the solenoid. To test the starter run a wire from the + on the battery to where the thin wire connects on the solenoid. (ignition must be off) This should activate the starter and turn the engine. If nothing happens the starter is probably at fault. Before removing the starter make sure that the engine is properly earthed as this could also give problems.
If the starter does kick in the problem is further "upstream" Most probable cause would be the relay. If you can locate it, replace since it is relatively cheap.
Starter repair is best left to the experts. Get a quote for a new starter before you have the old one repaired. You'd be surprised at how many times it turns out that replacement costs the same as repair.
Let us know if you've solved the problem.

Has this Jeep been modified at all?
It sounds like the shifter cable was reinstalled backwards.
Specifically the 4-Low "Not Climbing Well". 4-Low should give you the best torque and hill climbing ability.
Do you feel any "Binding" in the steering wheel (difficult to turn)?
Remember a Jeep uses real driveshafts and differentials to give you 4WD - you cannot engage 4WD or 4-Low on dry hard surfaces. It needs a little bit of slip between the wheels for turns.
Check you're fluids too.

Hit the starter with a hammer and see if the teeth are stuck if it works you should be able to drive for about a month or two but you will have to replace the starter eventually. Or carry a hammer with you at all times; and that will even quit working at some point and time.

vacumn pod on the front axel is stuck on. Jack up the front wheels spin both tires at the same time and see if the front drive shaft turns. If it does the 4x4 on the axel is engaged. The front drive shaft on these should not turn when vacumn pod is disengaged. YJ's have a split axel on the right side inner axel shaft.

you can also check the 4 wheel drive vacuum switch on top of the transfer case...got mine for 10 bucks from parts store...fixed the problem