Call an electrican to be safe, but if it were me I would start at the main panel (removing the front cover) and checking to see if there is a ground bus and if that bus is grounded (ground rod, water pipe etc) and bonded to the neutral bus. It's hard to imagine even in a somewhat older house this not being the case. My house built in 1945 had a well grounded fuse panel even though it only had two prong outlets in most rooms. I changed most of them out for three prongs and replaced the fuses with a breaker panel. Identify the breaker or fuse that services the outlet of interest and check to see if the wire has a ground associated with it. Romex has a ground wire and older BX cable is grounded via the BX conduit to the panel. I would remove the wall plate at the outlet and check to see if the ground connection on the outlet is connected to the outlet box (usually a bare copper wire screwed to the outlet box) and if the box is securly connected to the conduit or ground wire commming from the main panel. I would verify the connections electrically with a an AC voltmeter as there should be 110 Vac between hot and ground.
You get the picture. It's fairly easy to see where the safety ground stops or is disconnected if you know what your looking for. If I didn't, I would call an electrican.