Will:
Was the 35V hot to ground reading via a painted screw? If so check to see if you get a higher reading to some unpainted threads. A lot of older apartments were wired using conduit systems where the conduit "should" make a good ground. I suspect Rockvirgo's fudge job involved common wiring the ground pin to a neutral wire. Potentially hazardous, against the National Electric Code, and not recommended. Especially dangerous if the circuit is part of a "common neutral" confirguration where the neutral is shared between 2 circuits.
Was the 35V hot to ground reading via a painted screw? If so check to see if you get a higher reading to some unpainted threads. A lot of older apartments were wired using conduit systems where the conduit "should" make a good ground. I suspect Rockvirgo's fudge job involved common wiring the ground pin to a neutral wire. Potentially hazardous, against the National Electric Code, and not recommended. Especially dangerous if the circuit is part of a "common neutral" confirguration where the neutral is shared between 2 circuits.