welcome to the forums. chances are, your 4th gear is bad, which is causing it locking up. pretty common on the trx420's.
4th gear is no where near the friction plates..lol. all your gears are deep inside the lower case of the motor, which means : you have to pull the motor, split the motor, and go through the process of replacing/inspecting each one this way. expensive ?, sorta. each gear will cost a few bucks..this is for sure !. then you will need all new gaskets top and lower end, would be a good time to replace all oil seals while its apart, a new cam chain is always thrown in when I rebuild my motors, as I said..sense its apart ?..now is the time to do it !. depending on miles/hours on your atv ?, if a lot ?, I would toss in new rings/bored over, which means a new piston kit ( comes with rings ). this is not always the case, but !, it's better to do this now, then have to tear it all back apart down the line. as you can see..this all adds up cost wise. if you do it ?, then the cost isn't too bad, but if a dealership does it ?, you dang well better have a ton of cash in your bank account !..lol.Better yet, if it's the fourth gear that's no good anymore, is it expensive to replace? Should I just replace all gears and how do I go about changing it? How do I find it?