I'm trying to troubleshoot transmission problems on a 1997 John Deere 310 se we just put a new charge pump on the transmission and it's still locking itself out of gear it comes and goes

SOURCE: John Deere Gator 4x2 - Left Wheel doesn't move when in 2nd gear

I would replace the high/low switch and the reverse switch. One time a replaced the high/low switch and the reverse switch quit on me 2 weeks later.
You can also get the Peg Perego Gator Shifter that upgrades the vehicle.
You can get the parts and repair help at this site
http://www.shopjandl.com/kids---baby-ride-on-toys-peg-perego-switches-and-shifters.html
They have helped me several times.
Hope this helps

SOURCE: 2020 john deere diesel tractor with j-d 36# loader

Sounds like you need more hydraulic oil - Or like you said the transmission screen (dirty).
Where it is ??

SOURCE: john deere stx38 wont move transmission locked up?

Engine OFF, raise drive wheels and check if transmission is locked

SOURCE: john deere transmission what other mowers interchange

You will have to first know what kind of transmission you have. You will have to consider if it is manual or hydrostatic drive. The transmission model number should be stamped usually on the top of the transmission. Yes transmissions are interchangeable, for example some John Deere, Craftsmans and Husqvarna all use the same transmission. Peerless is a manufacturer of these, the only one I know of. So don't let anyone tell you that you can ONLY use a John Deere product. To determine what transmission you can cross over with, get the model and serial number off of your John Deere's transmission. Call a small engine repair shop and ask them what all transmissions it will cross over with. Let them know you are aware that Peerless manufactures the same transmissions for most all riding mowers and that they will interchange. If they are uncoperative, contact me with the model and serial numbers off of your transmission and I will cross reference it for you. But try to get model and serial numbers for other brands from them, then check these against used ones. You will need to tell them if it is a hydrostatic transmission or manual and if so what speed manual.

SOURCE: problem with John Deere L120 tractor

Park brake switch is the most likely culprit,any other would cause the tractor to not turn over in the crank position.