You may have a couple of things going on per your description. The cable attaches from the rear right. It may be best to pull the 5 retaining pins, roll the belt off the front, drop the deck and slide it out about a foot to the right. You will see a tensioner pulley that has a smooth end- that is where a 1/4" flat washer goes, then the cable spring, then a small hitch pin or cotter pin. To the rear, you will see where the plastic body of the outer cable slips into and is retained by a larger hitch pin. Re-hang the deck and install the belt. If all is working freely, the belt routed as it should be, and the cable is good- the belt should turn the blades. Now about the shutting off part. Does it seem like the when the deck handle is engaged, that a switch is shutting off the engine? The normal cause for this is an un-plugged or defective seat switch, but there could be other causes. Let us know how you do or if something seems different.

Well, simply calling it out as a Craftsman LT 1000 does not help anybody who might wish to help. The nomenclature "LT 1000" is a generic reference to an enduring model name. What is needed for getting specific information about "which" LT 1000 requires posting the full technical model number (typically begins as 917. and can be found under the tilting seat). Saying LT 1000 is like saying I have a Chevy Impala....Yeah? Which one?

***"On TDC the exhaust valve spring is at 1-1/8 in. out and the intake is at 1-3/8 in. out."*** I need to emphasize that "TDC" and "TDC on the COMPRESSION STROKE".......are not the same thing. So, having made that statement, let me ask this: When you are measuring the length/height of the valve springs...do you have clearance, or lash, between the rocker arm and valve stem of BOTH valves/rocker arms???. If yes, then you have most likely detected a displaced valve seat. If, however, you have no detectable clearance or lash at the valve stem/rocker arm of the "shorter" valve spring....the engine is positioned at TDC on the EXHAUST STROKE, and the camshaft is holding the exhaust valve OPEN, thus the "apparent shortening" of the exhaust valve spring. So, let's just double check that before we declare a displaced valve seat for sure. ***"Is this motor worth the money with about 1500 hours of usage?"*** That is something that only you can really decide based on how much you want to spend to rehab this engine. You can base your decision on "cost of repair $" versus "cost of new mower $" if you like, and consider that as an "objective decision" based solely on money spent at this time. But, you will still have an older machine that will have other things to fail/wear out down the road, and sometimes......you can second guess yourself to death in these situations. The bottom line decision you have to make is not so much about the worth of repairing THIS engine. It is about how much time/money are you willing to spend maintaining an older machine/engine? AND, whether you are personally capable of doing the work (or the bulk of it) yourself. As to a personal preferrence or recommendation of a particular brand of replacement mower.......I don't go there! But, there are many, many, many threads in this forum where the yays and nays of the different offerings of the market have been argued/debated/dissed etcetera. It almost boils down to "What color do you like?"

Remove the deck so you have a good unobstructed view of the ground drive belt system. Have a helper sit in the seat and push down on the clutch/brake pedal while you examine all the linkages in the mechanism from below the frame. You are looking for worn or loose pivots, pins or anything that can limit the travel of the components that put enough slack in the ground drive belt for the transmission input pulley and shaft to become "unpowered" so you can shift. Have you also noticed the clutch engaging at a lower pedal position when you try to get moving from a stop? That can also be a symptom of the same issue. If you have recently changed the belt and did not use an OEM spec belt there is a chance the belt is a fraction too short. Basically, something is causing a bit of power to be applied to the belt when the clutch is pushed down. Here is a link that might be useful: 917.272751 OM