The primary clue here (in my opinion) is what you noticed about the hour meter not coming on when you turn the key switch.
In most machines the hour meter is powered by the same circuit of the key switch that also powers the fuel solenoid (if equipped).
The fact that when your hour meter does not work and you also are unable to get the starter to operate, makes me think that the defect causing all this might be corrosion or a poor fit of the wiring on the backside of the key switch.
When you are inspecting the backside of the key switch be certain to examine each blade connector where it is riveted to the switch plate. The large connector will have to be unplugged from the switch to check the rivets. These rivets can get loose and when they do you will have problems as you described. The blade connectors may also show signs of burning or turning dark.
Try to gently "wiggle" each blade connector with a finger tip or needle nose pliers while you watch where the rivet joins to the connector. Use a magnifying glass if needed. If you find any looseness there replace the switch.
It could also be corrosion affecting the main fuse blade surfaces where the fuse plugs in.

If you do not find anything wrong in the first areas I suggested above you should then do a thorough cleaning of ALL the end terminals of the big battery cables (negative and positive) at the frame, battery, and at the solenoid.
If you must address the cleaning of cables part of this I would begin by first disconnecting the Negative cable at the battery and then go to the solenoid post where the Positive BATTERY cable connects. On most machines that post is also where the main fuse wire picks up its source of power to feed the key switch. Corrosion there on that wire can cause the problems you are having.
I would not replace the key switch unless you go through the entire clean and search procedure without any change of condition.

When you hear hooves think horses not Zebras.

Before you do anything test the battery and make sure the connection are tight... Die Hard batteries tend to die quick.

Zebras.
JAL might be right about it simply being a defective battery but my interpretation of the complaint description was that the issue is "intermittent".................and that word led me away from suspecting a faulty battery.

thanks mownie and justalurker.

i looked at the mower again with both your suggestions in mind.

the connections at the battery posts were clean and corrosion free, but a few screw turns loose on both posts. my hope is that this solves the problem. i started it several times with no issues, but will see how it goes the next few uses.

i was also suspecting a electrical connection issue at the key switch level as mownie suggested. did some wiggling around when i was experiencing the problem but did not find that associated with the "click" that was telling me the tractor was going to start. If tightening the battery connections does not work i look further into mownie's advice.

greatly appreciate your prompt replies.

Loose cable connections at both ends of the battery cables will be a problem.

In my experience Die Hard batteries are a problem waiting to happen.

Ignition switches on the late model JD Select Series have proved pretty reliable.

Might be that pesky time delay module.

Check to see that the charging system is working. Testing with a meter is a definitive test but here's a quick and EZ test...

In a dark area start the X304. let it idle, and put the headlights on. While watching the headlights raise the engine speed to WOT. If the headlights get brighter then the charging system is working.

ok, justalurker...will try that

Apparently when it works, it cranks FINE.
That means there's nothing wrong with the battery itself!

I'm with mownie on a bad connection.

CHECK the FUSE!
Basically, 12V will be supplied to the ignition switch from a the smaller + wire hooked to the starter solenoid.
There will be a fuse inline between the solenoid & key switch.
SO-
Either the fuse is making a bad connection
or
the plug to the key switch is ""
or
you have a bad key switch.