Update: Ok so let me say I'm not going to give you suggestions on what other others think when they work on a John Deer or tell you to check your battery which is beyond obvious which drive me nuts when folks post that stuff on forums (not here).
My original symptom was a only a click when I turn the key to start. I did hear the carb solenoid engaged on hte first click of the key, then turn halfway for the glow plugs to heatup and then to start but only got a click which I could not tell where that was coming from. I check the battery and measured the voltage when I turned to start and it read about 11.9, but was 12.6 with the key off. I assumed it was a starter and had it checked but it was OK too. The mower would turn over if I shorted the starter leads, so I assumed this forum thread was the golden key, but be warned that accessing this relay was almost impossible and I work on electonics all day. The entire board is entirely encased with rubber. I used a dewalt multi tool, box cutter, dental probes, heat guns, wire brushes, etc. Unlike the other post I removed the entire outer plastic casing to remove the entire circuit board by flush cutting between the rubber and the plastic which made this easier to get to the relay.
Three weeks working on this combo box to remove and search endlessly for a relay that meets the specs for this was nearly impossible since these are really small and have a high current rating, and I do not have a local electronics store. The original Mfg for the twin relay was found by doing a Google search TX2-8FZ had the specs but they appear to no longer be in business. Anyhow I removed and exposed the relays, cleaned with contact cleaner and tested with a 9volt battery and got good continuity when the relay engaged. I wish I tested these before I cleaned them because I'm wondering if they were even bad before that.
Long story even longer, I reinstalled the relay's and combo box and could no longer even get the carb solenoid to engage. I checked all levers and they were in the correct position. I took a tiny screwdriver and pushed the relay and the carb solenoid engaged but no luck in getting this to turn over. I then found all 5 safety switches and shorted them out still with no luck, so I then purchased the combo box locally for $240 because I did not want to wait a week for Messicks to deliver one online. New combo box worked on the first try with the switches reconnected.
This was a good suggestion on the relay because I'm all about saving a buck. My symptoms were worse, so it is entirely probable that I damaged another component in the box as I widdeled away on the rubber. (My combo box was the same PN but only had one connector, so I'm not sure why)
Hindsight advise: After talking with the mechanic when I bought the parts they said it was unlikely that the box was bad because these machine typically they see issues such as not turning off as well as not starting. They said it is almost always a switch that gets dirty, so
check all 5 switches first by removing the connectors and shorting them toward the combo box and the obviously check the 5 fuses, battery and starter. An attempt to get to the relay will be a challenge but if you do try this cut out the rubber around the relay where you see the TX2-8FZ part # facing up. The relay is enclosed in a plastic housing so a box cutter or exacto knife should go through the rubber but not the plastic. Cut flush against the relay housing on all four sides. Underneath you will need to removed 1/4inch of rubber around the area where the relay should be and then cut, scrape, wirebrush the rubber until the ckt board is exposed. Desolder the relay but note that the ckt board has traces on the top and bottom, so you must be proficient at using a solder iron. A full service manual would be extremely helpful for diagrams, locations and service instructions.
I have several more pics but could not upload multiple from my iPad for some reason.