Oof! 24 volts ! If you had it hooked up to that much power for more than a second or two there could be multiple fried components, especially if the protection diode didn't pop.
If the protection diode didn't pop, it wouldn't have let 24v past the power jack. Its when that diode does pop and stops shorting out that power can get past it and cause further damage.
The diode saves the radio, the fuse saves the diode. No more missing/foil/pen spring fuses!
Replaced the volume squelch knob and still no change
Whenever you have a catastrophic failure and think you have it sorted out, it is always best to run the radio on a current-limited supply and slowly bring up the voltage to make sure nothing else is shorted.
According to the 29LX LE schematic (only sch I have), the switch is the only way for power to enter the rest of the radio. If replacing that didn't help, I wonder if there is still something shorting inside causing the new switch to weld together.
Since it is now turning on and staying on, I assume you either found a good protection diode soldered across the inside of the power plug or you missed it and it is indeed an open and 24v did get past it. You said "protection diode
s", plural, so I assume you checked the diodes on the board and may have missed the actual protection diode on the power jack (if that is where they put it, and it often is). What is the current draw while it sits there powered on?
The power switch isn't in the volume pot itself, it merely rides the same shaft. Did you swap the entire Vol/Sq/SW assembly (or at least disconnect the wires from the switching section and check it's functioning with a continuity meter)? Those are not fun to find. You must have either had a donor radio sitting there (hopefully that one was ok, did you check) or figured out where to order an equivalent assembly to have replaced it already. I don't mean to question you like this, but a good switch will not let power into the radio. There is no other way for voltage to get past it to turn on the radio. So either it is not really replaced, the replacement was bad, or it fused again and you should have a large current draw and parts quickly warming up inside.