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.

Bill: Since at least the 1990s. Within the OPE arena Champ (easily identified) has for decades pretty much does OEM'd for all the OPE manufacturers (I'm aware of 2 small exceptions). Tell you what - why don't you show us someone the DON'T OEM to... If Allied Signal has made inroads this is a new development.

Have you removed the deck drive belt from the PTO? If yes, does the motor still die when it's hot with the deck drive belt off? If no, then remove the belt and see if the motor dies. Try new plugs correctly gapped. I've seen coils lose spark when hot. EZ to check... use insulated pliers to remove one plug wire when it's running funny. If it dies then that side is working. Try the other plug wire. If it stays running then you found the side the problem is on. either coil, wire, or plug.

***"I suspect my ECU was fried by the mere act of jumping it or because i connected pos to pos and neg to neg as opposed to neg to ground."*** NO! Whether you connect directly to the battery posts with both cables (whether charger leads or booster cables) makes no difference to the ECU (electrically speaking). The instructions telling you to connect the negative lead to a good ground on the engine is for YOUR SAFETY, not for the machine's welfare. The instructions are actually a sequential set of steps to perform in a SPECIFIC order that will prevent the battery from exploding due to an arc/spark that occurs when the LAST cable connection is made. By making the last connecting point somewhere away from the battery per se, you deny the explosive battery gases a source of ignition. If you inadvertently left the key switch of the X 304 turned on when you were making your jumper connections, that might have caused a problem similar to what tomplum has observed with finger tight battery terminal bolts.