Something is fishy here......
A seized transmission (it's actually the agitator shaft in the upper housing, not the transmission itself) in these machines will not agitate but WILL spin. Conversely, a seized tub (due to jamming, seized tub bearing, stuck brake package, ect) will not spin but WILL agitate. Basically, it should be something. If the machine does nothing, it's a timer/motor/lid switch/wiring or electrical problem.
I'd be leery about taking advice from a repair person, especially if they're under 50, as most aren't well versed on these older machines and it's easy to misdiagnose the problem or just claim "Yeah, it's dead" when they come up empty handed, take your money, and move on to next victim......err....customer.
Lets confirm the transmission:
Grab a 4X4 piece of wood (or something solid and similar in size), tilt the front of the machine back and stick it under the right front foot.
Locate the center pulley. Slip the belt off of the pulley if it's still in place (looks like you removed the belt in your earlier posting).
Grab the center pulley and turn it COUNTER-clockwise.
Report back if the pulley is easy to turn, difficult to turn, or is seized up.