It's common for the MTD solenoids to go bad. They are kinda wimpy and OEM are overpriced.
I've had good luck buying these recently from ebay
**CLEARANCE PRICE** 33-335 Solenoid 3-Post equal/ MTD 725-1426 1-8817
They are the 3 terminal type at $8 with free shipping.
The new ford solenoid you installed should have worked ok, it's heavier duty and usually cheaper in price as compared to the lawn mtd lawn tractor types. (your ford unit is hanging on (sticking). Most of the standard ford solenoids can be used to replace the MTD 3 terminal type starter solenoids, but if yours requires a 4 terminal lawn tractor solenoid, you need what is termed a Isolated base ford type solenoid. (this means the 4th terminal is isolated (not grounded) to the solenoid base. (the 4 terminal is usually is connected to or thru the safety switches) You also have keep a heads up when installing solenoids, especially the ford type, but generally all starter solenoids. The ford types and some others have one lock nut close to the stud terminal's base on the terminal stud bolts, If you loosen this single locknut or allow the small or larger stud bolts to rotate going inside a solenoid (or starter) when installing or removing the wiring the solenoid is usually ruined internally or it's life shortened. When installing the connecting wires to a solenoid I do not use a socket wrench, I use open end wrenches so as I can watch and keep from turning the solenoid studs. (sometimes this requires the use of the small thin type ignition wrenches on the bottom lock stud. If the stud turns going inside the solenoid it usually ruins and solenoid or shortens it's life. I had a guy bring me 4 of the new Ford type solenoids and he wanted to know what he was doing wrong installing them. He was twisting (rotating) the studs using a socket wrench and the stud was turning inside the solenoid and ruining the NEW solenoids internally. Some Ford type solenoids come with only one nut on the small terminal studs because Ford uses PUSH on terminal connectors, not ring terminals and if you remove this single locknut to install a terminal wire and the terminal rotates when installing it will ruin the solenoid internally, usually.
I suspect your eq. will operate ok if you will install a NEW correct type solenoid and make sure all your terminal are clean. I also use a box or open end wrench when removing and installing starter terminal wires, paying attention that I'm not allowing the bolts to rotate that's going inside a starter.
