I have a 2002 s10 4wd will not work

Sounds like something is really messed up in the transfer case. First check that the rear driveshaft is intact and fully connected to the transfer case. If so, the transfer case needs to be repaired/replaced.
In 4hi or 4lo, the front/rear 'differential' is locked, so both front and rear driveshafts should receive power. In AWD, the power is supposed to be divided between front and rear driveshafts, but will allow power to go to the shaft with the least resistance (like non-positraction rear end will allow the tire with the least resistance to get all the power). If the rear output shaft is broken, or the rear drive shaft is broken, all the power is going nowhere in the transfer case.

Most likely cause is the encoder motor on the transfer case.

stop put in nuetrul put in 4hi or low shift in to drive pull forward slowly it should kick in

this all prove that engine and transmission co-ordination seems to be poor.

1. check accelerator sensor.
2. " accelerator pedal--transmission ctrl liver.
3. " transmission oil level.
4. " proper grade of transmission oil.
5. " pressure ctrl walls

If its a 4WD there is either a push button on the dash left side of steering colomn, its marked 4hi. If manual shifter in on floor center console. Pull back on lever to second notch marker 4hi. If you are in 4lo now and can't get out. first put tranny shifter in neutral while engine running, then shift transfer case into neutral (manual push forward), push button hold 4hi and 4lo at the same time til "N" green light comes on. Then shift either into 4hi.

It is the buttons. It is about a $50 part new on ebay. Easy to replace. Just pull gently on the dash bezel. I believe there are two screws/bolts. Pull it out and disconnect the wire harness. Then just plug it in and put it back together.

Check the U joints on drive shaft & both front axles.

Try jacking up one side of the front and putting it on a jackstand. Then turn key on(but dont start it) and put it in 4hi. Try to spin the tire in the air. The drive shaft should not turn nor the wheel. If the wheel does then maybe the acuator is not moving in the axle. It worked when you pulled it out but it might be hanging up on something in the axle.

You should be able to put in 4x4 while in drive less than 35mph. Mine had a switch to turn to engage or dis-engage.

try seeing if the cable going to the front differental is pulling in to engage the front axle?