In order to install a 3 prong receptacle you MUST have a ground in the box, otherwise you can install a GFCI receptacle. This will provide a 3 prong plug but still will not provide a ground.
If the cable that supplies power to the receptacle box is armored cable then a ground MAY exist in the box. To tell you need to buy a neon bulb voltage tester or a multimeter. You measure between the hot wire and the metal box. If you get either 120 volts or a light on the tester then this indicates a ground is present in the box. Then you can install a 3 prong self grounding receptacle in place of the 2 prong. Self grounding receptacles are sold at Home Depot and indicated on the box to be self grounding. If you want to install a regular 3 prong receptacle and not the self grounding type, then you must pigtail a ground wire to the box using a 10-32 screw.
Your other option is to run a new circuit to the living room that has a ground and install a new 3 prong receptacle.
Here's a link that'll explain all of this to you and under what conditions you can replace a 2 prong with a 3 prong.
http://www.codecheck.com/250_50_commentary.html
A self grounding receptacle has a special clip on the yoke and will look like this:
They don't require a pigtail ground wire be installed to the metal box. But, like said above, you are not allowed to install a 3 prong receptacle in place of a 2 prong unless the box is grounded. Your existing 2 prong receptacles are fine to use unless you want to run a device that requires a ground, such as a computer.