You really should download the service manual, before you start spending any money. The solenoids can "fail" in circuit operation for any number of reasons, only one of them is a bad solenoid.
I'd recommend you download the 2000 LX470 manual I posted; it's bookmarked and more easy to use than the 100 series manual. You won't be missing anything because you don't have the "Land Cruiser" service manual. Normally I would recommend the opposite, but in this case, since I use this manual all the time, I can recommend it without reservation.
Make sure you have the correct code; P0770 isn't a A343F diagnostic code for the 2000 A343F:
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You'll have to pull the pan in order to check the solenoids, so you need a tube of Three Bond 1281 [08826-00090] and a drain plug gasket [35178-30010], get several. You'll also need transmission fluid. If you don't know if or when the transmission was flushed, I'd recommend you plan on doing that. Drain the pan, remove it, test the solenoids and the pigtail, make any R&R changes necessary, reinstall the pan, and then flush the transmission. Using the cooler lines at the radiator, you will be able to flush the entire system, less the torque converter. The instructions are floating around here somewhere.
Jegs and
Summit regularly compete for the best prices:
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If you really feel like you have to replace the solenoid, here it is:
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