The engine on the left is not a PS2 engine. I believe that's what MTH called LocoSound which did not use a battery. I don't have any LocoSound engines so can't help you with the locked-in-forward issue.
As for the PS2 engine on the right, if the sounds cut-out as soon as you press the DIRECTION button, then it's almost surely a battery issue. If you have another PS2 engine that has either a dual-AA or dual-AAA battery I'd swap the battery to see if the locked-in-forward problem follows the engine or the battery. A PS2 engine that is locked in forward (requiring the Bell-Whistle button reset procedure) will upon application of power behave as follows: faint relay click coming from the circuit board, then engine sounds start for a few seconds, then engine starts moving fwd proportional to throttle. You need to solve the battery issue first. That is, even if you successfully reset the engine (to take it out of Fwd lock), you need the battery to "save" the reset as well as to cycle the engine thru the Fwd-neutral-Rev-neutral sequence when you press the Direction button.
