Tom, ..
First off, remember, YOU are my eyes & ears, it's difficult to try helping someone fix something on-line, so I need you to understand, your mower is not in front of me. I will continue to do what I can to help, I'm grateful for your patience, and the fact ,it appears you have mechanical knowledge and are not afraid to get your hands dirty. And there are many other members here with a hell of a lot more knowledge than myself,(some are dealers ! ) That being said .. lets get to work,
the new solenoid now at least clicks, OK this is what I would do, .. first check the oil, we don't want to waste effort on a seized or blown eng. next I would pull the plugs, and see if I could turn the flywheel by hand, ( hopefully you can ) here is where I'm reminded about the blown fuse, it coulld have blown from something "locked-up" or just a short in the wiring.
Next, take a known GOOD charged battery and jumper cables, attach the POS. cable to the Batt. POS. and to the eng. starter input terminal, ( yes I know it's old territory BUT I'm not there , remember ..?? ) THEN, connect the NEG. cable end to either the mower frame, or on an engine bracket, or block, whatever.. making VERY SURE the connections are CLEAN & snug, then hold the end of the NEG. on the NEG. battery term, hopefully the starter spins the engine ... and quickly, ... if not, I would remove the cables, then remove the starter, and test it off the engine, I'm sure you know how to do that, hopefully it's good, if not, I would suspect that may have caused the fuse to blow, with the starter off try to rotate the flywheel, is it turning freely or dragging, ( is the BLADE ENGAGE lever in the OFF position ..?? ) If it's dragging we have other issues, IF the engine rotates easily, and the starter checks OK, then I would reinstall the starter, and reconnect the battery (in the mower) being VERY SURE the cables are NOT worn, or frayed and have CLEAN TIGHT connections, ESPECIALLY, the GROUND cable ! RE-check the voltages at the battery itself, then at the solenoid (AGAIN) , if all checks out OK, try to start with the key, if NO-GO, then I would remove the wire harness connector from the IGN. sw. ( yeah I know it's a (PITA) ) but .... then "jump" the battery and solenoid terminals of the harness connector (should be the RED & ORANGE terminals, (use a piece of wire of decent size, or a pair of needle nose pliers) IF .. it rotates the eng. GOOD, !! I would then suspect the IGN. sw. is bad, then, I would reinstall the plugs, and move the throttle lever WIDE-OPEN, and pour a small amount of gas into the carburetor inlet, ( best to remove the air filter to do that, NOW try to crank it with the jumped IGN. sw. if no go, I would suspect possibly the mag, is grounded out. OR ??? ... hopefully it will fire-up briefly, but let's get this far, and see what happens, OK ..?? Sorry if you think I'm trying to treat you like a "dip-schitt" but as I said ..YOU are MY eyes & ears now. I'm trying to HELP YOU ! so bear with me Tom !..:thumbsup: