When you start it, it back fires through the carbarater , its a 88 chevy s10 2.5 4cy.

Can you hear the pump buzz when cycling the key ?

You may adjust the High adjustment screw on the carbarater most of the time carbarater needs to be rebuilt.

Could be a number of things. Dirty gas tank, timing belt, carbarater. It sounds mostly like the carb.

sounds like the carb may have blocked jet(s), worn diaphram ,air leak ,incorrect fuel/air mixture any of these will cause your problem , have the carb overhauled

Start by replacing the starter solenoid or just the whole starter as it appears the solenoid is not making good contact.

WHAT I WOULD DO IS TEST THE FUEL PRESSURE SOME TIMES THE PUMP WILL PUMP ENOUGH FUEL TO GET TO THE TBI BUT NOT ENOUGH TO FIRE THE TRUCK. IF FUEL PRESSURE IS GOOD REMOVE THE DISTBURTOR CAP AND INSPECT THE CAP AND ROTOR, CHECK FOR CORROTION N EITHER ONE SOME TIMES IS BUILDS UP AND STOPS THE SPARK. GIVE THAT A TRY GOOD LUCK HOPE THIS HELPS.

got a 88 chevy 1500 4x4, new bulbs & new fuse but no brake lights?

Distributor get taken out? Sounds like it's one tooth off at the gear between the camshaft and the distributor shaft.

Your timing is over advanced,if this problem has just started occuring,the timing chain has probably jumped.

sounds like tbi has gone out on it thats what happend to my 88 silverado