Riding Mower is turning over, but no spark and no fuel solenoid click

Hello, I am hoping someone might be able to point me in the right direction. I picked up an old Craftsman Riding Mower with a Kohler Engine.

The reason they didn’t want it anymore, is it wouldn’t start; however when you put some starting fluid in the carburetor it would fire up for a second. So after doing some research I checked the fuel solenoid and it was so full of gunk it would barely move. So I just went ahead and picked up a new one and while I was at it, grabbed a new carb as it was so cheap. After I cleaned up the engine, put a new spark plug in it and installed the new carb, it fired up, and while the governor was a little touchy making it surge a little here and there at higher RPMs, it was working fine. So I started doing a test cut around the yard and when I hit the thicker grass it bogged down and stalled out on me. So I raised the deck and disengaged the blades and went to start it back up, and it turned over and over but never would start. So I assumed I flooded the engine and let it sit for a while and came back to try it again about an hour later and still, turns over but doesn’t even attempt to start, which by then it was getting late so I pushed in the garage for the night.

Today I went back out and checked it again, and still it wouldn’t start. So I tried shooting some starting fluid in, and it still didn’t try and fire. So I pulled the Spark plug and put my finger over the hole and spun the motor and felt the compression push the air out and try and suck it back in just fine. Next I grounded the plug on the engine and turned the key and there was no spark at all. Thinking maybe it was a bad plug (even though it was brand new) I put another plug on and grounded it, still no spark. Lastly I pulled the fuel solenoid off the carb and turned the key to see if it retracted as it should when the key is turned and it didn’t move.

So I am stuck now on what to do next…. I was thinking of trying to figure out if this was a kill wire sort of thing, but since it turns over I wasn’t sure if a kill wire would still let the starter crank on the thing. I know if the clutch isn’t pressed or the seat pressed on while engaged, it won’t even turn over when those kill switches are stopping things. Also… I am uncertain if it would be the coil or something else related by the engine, as the fuel solenoid should engage the moment the key is turned to the on position.

Any thoughts? I greatly appreciate any next steps anyone might have for me. Thanks!!