Unless you have a lot of money to spend..........DO NOT BUY "Starting Fluid". Commercial starting fluid is ETHER. Ether is much too explosive and violent to use in a small engine such as the ones we deal with here. It's not that ether is expensive, it is not. But pistons and heads add up real quickly, same for rods and crankshafts!! Use spray carburetor cleaner instead (Carb Medic, Gumout, et al).
QUESTION: Did you use a genuine Kohler fuel filter, packaged in a genuine Kohler branded package or carton? If you did not use a genuine Kohler brand fuel filter, that might be your problem, I mean....the engine's problem. By popular consensus of most members of this forum, Kohler engines are very picky about their fuel filters. You almost have to "show them" where it says "Kohler" before they will be happy.
The fact that the engine ran ok when you "straight lined" it makes this situation lean toward a fuel filter issue. There are some fuel filters being sold that literally create more problems than they prevent. This seems to be especially true with Kohler products. Lots of folks think you have to buy the dinky little filters offered at the small engine shops or home center. Not true! You can buy a large size fuel filter at any automotive parts house that will perform well on a lawn machine. You need to choose a filter that has nipple type hose bibs of the same diameter as your old filter. You also need to stay away from filters that are intended for use on fuel injected engines. Those filters have denser media to catch smaller particles and they require a more powerful pump to get fuel flow volume through them. Fuel injection filters have metal bodies, carburetted filters are plastic. You must also check the filter body of any filter to see it there is a "directional arrow" indicating which way fuel will flow through the filter. Some filters incorporate a check valve, or have a "biased media" that only wants to allow the fuel to flow in one direction. Just some thoughts and things for you to check or consider.

Originally I did put in a generic fuel filter - which is when the problem began. I then got and installed a genuine Kohler filter, which didn't seem to make a difference. I did make sure the direction of flow was ok. I'm going to try putting the gas line with the Kohler filter back in and see if it starts at least.

good you got back to kohler for the filter, but make sure it is the "right" type for your app... kohler also offers a cuppla different micron ratings - the wrong one could starve your engine for fuel no different than if it was stopped up.

also, did you install new fuel line(s) - older machines fuel lines can start to deteriorate letting chunks of wall stuff get right into yer carb.

what about the gas cap - is there a hole in it which has become clogged... Try running it with the gas cap loose .

( Why is it that these problems dont happen in the middle of January - when you dont need to mow the lawn :)

Good luck -- Dave