Thanks everyone for your replies. I'm not going to reply to each individually, but I do appreciate your ideas and am going to look into each one.
I'll be mowing again Monday or Tuesday. Tomorrow looks dry, so I'll roll out the mower and do a few things to it. Me and the previous owner never used the Left tank so I'm going to block it off with shut-off valves I have, drain, remove, inspect and flush it out. I'll do the same to the fuel line and filter. Reinstall and use only this tank to the carb. If it dies, that is ruled out. If it doesn't die, I'll repeat the cleaning process with the primary tank.
If it does die, I'll check the spark on both plugs (new). I have one of the testers that you hook up; I'll just have to read up on how to use it. If I don't have proper spark on one or both, I'll order a new set of coils.
If I have to install new coils, and it still dies. I'll finish the yard in sessions as I am doing now and the remove the carb and clean it. I'll check that out on the following week. If it still dies, then a new carb.
Did I miss anything?
Thanks
P.S. Forgot to mention, the solenoid is new.