'94 Ford Explorer-Stops, won't Start again

Hi all,

I've got a 1994 Ford Explorer Sport (2-door, 6 cylinder engine).
Within the past few months, it's begun to die on startup.

Symptoms:
The engine can be heard firing up, but after the initial startup, there
is a rumbling sound and shaking, and then the engine dies. It will
continue to do this unless I leave it alone for anywhere from 15 to 30
minutes (possibly more-not sure. I never timed it). Then it will
start normally, and I can drive off. It never happens while driving or
idling. It also doesn't happen in the morning when I go to work, or
after work to go home. Presumable because of the extensive time in
between. It only happens when I shut the engine off and then return to
within a few minutes. In recent months the car can be counted on to do
this fairly regularly with the exception of a span of time ranging from
this weekend to today due to some replacements I've made. Today was an
uncomfortable surprise, and one I'd like to end.

What I did (so far):
A few weeks ago, I replaced the fuel filter (or actually, had it
replaced by a local shop; the filter wouldn't come off manually, and I
didn't want to damage anything trying to force it.) A week or so prior
I replaced the air filter. This weekend I replaced the spark plugs,
spark plug wires, and the battery. I had thought the battery the
culprit because it was old and, prior to this weekend, the last time I
was having trouble was when the engine wouldn't start at all. So I
thought it was the battery and replaced it. Apparently I was wrong.

I don't know what else to check. I'm no car guru, and I was told it
was either fuel congestion, electrical problems, or both. What I'm
looking for is information on what needs repair, and if I can do it on
my own without going to a shop.

Thank you for your help!
Erik