Here's the upshot on the John Deere 455 with the non-func tranny.

Check out the hydraulic schematic on www.tufftorq.com if you're
interested in seeing the logic; chase down through the service links
until you find the service manual for the K92 transaxle.

The prior "mechanic" had welded shut the actuator pins on both "tow"
valves. For good measure, he brazed the balls in their seats.

The tranny had low-power forward, but no reverse. Since the same motor
and pump provide both directions...

Look at the drawing, and you'll see that the hydrostatic gets its fluid
charge through the two valves he welded shut. It can suck some fluid
through the "anti-cavitation valves", but would never be able to fully
purge the circuit of air unless the charge is provided under pressure --
which it could not be with the tow valves soldered shut.

With some small trepidation, I ordered new valves - $353 worth - and
screwed them in.

Tractor runs great. Now I have to pull it all apart again to fix the
fifteen other leaks that showed up after about a half-hour of mowing! AND
the twenty or so worn out bushings in the chassis. AND the wiring
harness. AND..... G

Hey! The tractor went for $15K new, and I got it for (net, now) $353.

LLoyd