yes you definitely have a problem.
the power switch in the 2000GTL switches ground and should not have any voltage present on the switch terminals.
either something is connected wrong or you have a shorted component.
if you want to fix radios, you can't get away from learning how to read schematic diagrams.
here is a shot of the section of the 2000 that you are dealing with:
notice S401 and that it is connecting a ground on the power supply board to the main PC board when it is turned on.
If C302 on the power supply board was shorted, then you would get the problem you have now, but that doesn't necessarily mean that's what you have going on.
could be other things.
start your search for bad components on that little power supply board, which includes that big transistor underneath the radio.
do a google search for how to test transistors with a multimeter.
you will have to unsolder the parts from the board before you test them.
testing capacitors and resistors can also be done on a multimeter, again google is your friend here.
LC