Don't know where this will fill into the thread exactly, but here goes....
I have the same problem (May 2015) with my 2005 MF 1533. Checked fuses, seat switch, checked for water in fuel, removed fuel filter, etc. - all good. Checked voltage on 3 prong stop solenoid supply connector. The voltage (+ to -) on plunger retract prong (with key on) is good, The voltage (+ to -) on plunger insert prong (with key off) is good. Removed the two solenoid bolts (metric allen head on mine - 4 or 5mm) & took solenoid off....Tractor fired right up. I pushed plunger in on fuel injector pump to kill engine. Also killed it with the fuel shut-off on the bowl, & by killing it in high gear. No oil seems to be leaking out near the injector pump plunger but I won't really use the tractor until I get it fixed. Checked price for new solenoid at MF dear - $220 + shipping! Crazy. Saw some knock-off solenoids on eBay for $22 (free shipping) but not enough info to tell if plunger size is the right diameter/length. Can't find any cross reference info either. I checked the Woodward website which was no help. Anybody know of a cheaper fix? $220 is outrageous! Also, Rubber boot showed a little melting. Removed boot from solenoid with tiny screwdriver in an attempt to see if I can fix the solenoid but there is a printed circuit board in there with some computer chips on it- I'm not smart enough to fix.
