No start or crank on 1987 s10 4x4..Replaced battery and alternator..Fusses look good and I can put a screwdriver across the screws on the starter and the starter will wind but not start.

Have you checked actual voltage readings? Use a digital multimeter. Make sure battery has a full charge and battery connections all good. You could have a voltage drop on some of your connections? You have a starter relay on fender lining? I looked up your starter motor, 5.oL engine, no solenoid on top of starter.
You need to check ground circuits, also. Your starter motor grounds through the engine block.

At the starter relay, if voltage and ground are good, you could take two large screwdrivers, touching the two large terminals on the relay, let the shanks of the screwdrivers touch, the starter motor should crank. You don't need to use the key. There are safety issues when trying this, you have to be sure the tranny is in park or neutral and functional parking brake is set, block the wheels. Safety is your responsibility.

There could be other issues?

Take your battery somewhere and have it load tested. If it tests good it has to be your starter. The alternator has to be working or you would have a dead battery all the time. Unless you are putting it on a charger or jumping it.

There are 2 cables connected to the starter the one from the battery (the thick one) and the one that feeds 12 volts from the ignition that is the thin one. Probably the one from the ignition is not sending 12 volts to the starter. You can get a test light to verify that or test with a piece of cable connect one end where the thin wire from the starter is connected and the other end briefly touch the positive post on the battery. If it cranks then is the ignition switch not sending 12 volts to the starter. Or get a test light (it looks like a screwdriver with a tip) connect the black wire to any ground and the tip on the connector have someone to crank it up if it lights, is good if not is a bad ignition. Don't know how to do it get an electromechanic. Hope this help

short across the big terminals of the starter solenoid and it the starter spins then the problem will be in the light wires that operate the starter solenoid.

Is the engine locked up ? Before i replaced all that i would have put jimper cables on the battery and jumped the starter with a screwdriver to see if it worked and the engine turns.

Does the engine spin over and not start? Or turn the key and nothing happens?
New spark plugs and wires won't have anything to do with the starter and battery keeping the engine from spinning when you turn the key.
Need more specific explanation. Thanks,
Scott

No crank means dead battery, jump it or get a new battery. If your battery was not dead and you didn't get fuel or it did not start you would get a cranking noise and no starting

YOU SHOULD HAVE YOUR BATTERY AND ALTERNATOR TESTED.IF THEY DO END UP TESTING O.K,THEN YOU MAY NEED THE STARTER SOLENOID THAT BOLTS TO THE CAR ,NOT THE ONE ON THE STARTER ,REPLACED.YOU CAN CHECK IT BY CROSSING IT OVER WITH A SCREWDRIVER ACROSS THE TWO LARGE COPPER POSTS,IF THAT MAKES THE CAR START,THEN REPACE IT.IF THE CAR STILL DOES NOT START,MAKE SURE YOU HAVE A GOOD GROUND TO THE STARTER.

If your starter is drawing too much amperage and/or you have poor spark this can happen. Starter will steal necessary amperage depriving ignition system of voltage necessary to operate. To check starter draw, first load test your battery to make sure it is good, then put a volt meter across the battery and crank it over. If voltage drops below 9,5 volts, the starter is drawing too much and needs to be replaced. If it checks out good, check the coil for spark output. spark should easily jump a 1/4'' gap and have a good "snap" to it (not weak and fluffy orange spark)

Your starter needs a "makeover". try to clean or change the brushes in the starter.

a cheap and simple solution, is to make the cables on the starter longer, and attach them to a button in you car. If you choose that solution, you just have to turn on the ignition, and then push the button you have connected the starter cables to.