I wouldn’t jump to that conclusion yet (that your dc jack is bad). Didn’t you say you were getting 9V on the solder joints of the 9V jack? If so then your jack is fine.
The “sides” of the switch that Roy was talking about are the front and back side. You should be getting 9V on the center lug of the switch (the center lug on the half closest to the DC jack). When the switch is on (pushed in) you should then get 9V on the lug of the switch furthest away from the front edge of the board (closest to C1). These lugs should be connected when the switch is in, check this with your continuity tester.