I have an 1990 Econoline E-150. It has never started exceptionally easy. It's always taken about a second of cranking to start. Recently, it's been harder to start (takes more and more cranking to start) after driving for a while or having started it recently--kind of a combination of the two--the longer it's been driven and more it's been started within the last hour, the harder it is to start. When it is cold, it starts pretty easily.

I replaced the starter twice, upgrading to a fully rebuilt after the first partially rebuilt didn't alleviate the situation. I replaced the battery too as all the excessive cranking wore it out. That helped matters a bit, but it's back to it old tricks. If I make several stops at different stores for example and don't take very long in any of them, it becomes impossible to restart. After letting it sit for 15 minutes to half an hour, it will start grudgingly. When it is cold, it pretty much starts right up.

The latest is that it will not start at all after charging the battery nor with a jump from another large vehicle. It will make a solid click. Battery seems to be holding a decent charge. Water levels are good in cells.

Is there a relay that might be the likely culprit?

I did replace 6 of the 8 spark plugs about a year ago. I was not able to get to the last two with enough leverage to remove them.

 

Which 2 spark plugs were you unable to get loose, There is a reason I'm asking.
From what you describe , it sounds like there is a problem either with the battery cables or the connections where the cables connect to the vehicle, providing the starter is OK.
The relay where the positive cable from the battery connects to could cause the problem.
A simple test you can try is to turn the headlamps on and attempt to start the engine.
Watch what the headlamps do. Do they go dim, or do they do nothing.
If there is a bad cable connection (could be corroded internally) the lites should go dim if not, the relay is suspect.

 

Just a thought. Easy cold start and hard warm/hot start sounds like a weak ignition coil. A weak coil can fire the plugs under compression when cold as the timing is retarted, thus less compression. When warm/hot, the timing is advanced, thus more compression and harder for a weak spark to jump the plug gap.

 

Is the 1990 fuel injected or does it have a carb? I don't know what year they switched over. My '85 has a carb. On the carb ones, I would look at the choke.