1985 S-10 Durango not starting...

My brother-in-law has a 1985 Chevrolet S-10 Durango (The only Durango I heard of was from Dodge.). Anyway, it's having some starting problems and I have cancelled out a few hunches and I need help on what to do next.

When it's cold I turn the key and I hear nothing, no start, just silence. I pump the gas a few times and it ignites and starts. I turn it off and on a few times with no problems. Then I let it run, until it gets hot and turn it off. I try to start it again and this time I get nothing at all. It's not even trying to start. I turn the key all the way and I get silence.

I know it's not the battery, because all the accessories still continue to work fine and the battery was replaced about 6 months ago. It's not the alternator, because that was replaced about the same time as the battery and I had it tested. The spark plugs where nasty, so I told him to replace those, which he hasn't done yet. I figure the problem is more than just spark plugs am I right? I suspect the starter, starter solenoid or the ignition switch. I'm trying to help him out, but I just don't have much time to spend diagnosing it. Does this problem sound familiar to anyone, or is there a "no brainer" solution? Thanks

Well 85 was still carburated, so it's a manual fuel pump located on the front, bottom of the motor.
So you won't hear the fuel pump.

If you don't hear the starter turning over it could be the ignition switch, or starter, or the big wire going to the starter.

The starter solenoid is built into the starter.

It shouldn't be too hard to test with a multi meter

could always try jumping the starter solonoid with a jumper wire or a screw driver , if it doesnt sound like it does normally , hteres your prob , how ever , if it starts normally when you jump it , your problem lies else where