Transmission will not operate

Question edited for clarity.

Support ' Manuals - Murray

https://www.murray.com > en_us > support > manuals
Looking for support of your Murray mower or garden tools? ... search window below to locate Operator's Manuals, Illustrated Parts Lists and Wiring Diagrams.
Missing: 40371x50a ‎' Must include: 40371x50a

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  Manuals - Service & Support - Murray

  https://www.murray.com > en_mx > support > manuals
  Model numbers on Murray riding lawn mowers are found on the back of the mower ... to locate Operator's Manuals, Illustrated Parts Lists and Wiring Diagrams.

Inspirational Murray Riding Lawn Mower Wiring Diagram

https://www.pinterest.com > ... > Subjects > Science
Murray Tractor Ignition Switch Wiring Diagram. Riding Lawn Mower Electrical Diagram. Craftsman Riding Lawn Mower Parts Diagram - Amazing Wiring Diagram.
Missing: 40371x50a ‎' Must include: 40371x50a

425017x78B, Lawn Tractor Parklands Sentinel (2008) Parts ...

https://www.jackssmallengines.com > electrical-system
Murray 7800302 - 425017x78B, Lawn Tractor Parklands Sentinel (2008) Electrical System Exploded View parts lookup by model. Complete exploded views of all ...
Missing: 40371x50a ‎' Must include: 40371x50a

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  Lawn Tractor (2004) Parts Diagram for Electrical System

  https://www.jackssmallengines.com > riders > 42-cut > e...
  Murray 425001x8B - Lawn Tractor (2004) Electrical System Exploded View parts lookup by model. Complete exploded views of all the major manufacturers.
  
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Try the parts diagram, item 52 disconnect rod.

https://www.jackssmallengines.com/jacks-parts-lookup/manufacturer/murray/2002-models/lawn-garden/riders/lawn-tractors/42-cut/425613x8a-lawn-tractor-2002/drive-assembly

Anon try making sure you have fresh fuel in it and all the starter points and firing system is clear from corrosion that may be fouling it.

I was not able to find a manual but this may help.
It takes a while to download . Notice box at top with engine in it and a small down arrow that opens a dropdown list for other parts of the machine.
I hope it helps.
http://www.rayssmallengine.net/pages/oemparts#%2fBriggs_%26_Stratton_Yard_Power_(formerly_Murray)%2f624509x4A_-_Dual_Stage_Snow_Thrower_(2001)%2fEngine%2f624509X4A%2f11738

Clean the plug, clean the air filter, make sure there is clean fresh gas in the mower. If it has been sitting all winter with old gas in it, it may have gummed up the carb, but try the above before you venture into rebuilding the carb.

Try Sears Parts Direct.com or Parts Tree.com

Should be a adjustment bolt with a nut and spring that leads to the transmission

sounds like a plugged jet in the carb

hi this will depend on a few things, i will write all the data you need, you will have to see what yours is,
automatic transmission fluid ZF transmission: 3HP22/4HP22/4HP22EH/4HP24 = DEXRON II A5S 310Z (5HP-18): Black Plate = DEXRON III Green Plate = Lifetime oil/ESSO LT 71 141 A5S 325Z (5HP-19) =Lifetime oil/ESSO LT 71 141 A5S 440Z (5HP-24) =Lifetime oil/ESSO LT 71 141 A5S 560Z (5HP-30) =Lifetime oil/ESSO LT 71 141 Black Plate = SHELL LA 2634 Green Plate =Lifetime oil/ESSO LT 71 141 GA6HP (6HP19)/GA6HP26Z (6HP26)/GA6HP32Z (6HP32) = SHELL M-1375,4
total drain and refill 3.0 ltrs
sorry its so confusing but you gotta make sure you have the right oil for the right gearbox...hope this is comprehensive for you

Dave I have checked with a couple of companies and that part is no longer available. It is Murray part and they were taken over by Briggs and Stratton several years ago. Sorry
Good day.