Outlet is "Open Ground" - Is There Still a Safe Way to Connect to My Audio Gear?

This may be a silly question, but have you looked inside the outlet box to determine if there is a two wire + ground cable entering the box.  Unless your house is very old, it would be surprising not to have a ground wire.  Maybe it's there and not connected properly?  I can't think of another reason to be having an open ground.  Cheers. 

I assume that the receptacle is standard 3-prong and "Open Ground" was read from a plug in outlet tester.

What you can do is remove the outlet and check the ground connections. Sometimes the grounding wire is wrapped around a screw on the box and not to the receptacle and the installer assumed the ears of the outlets would make a good enough ground contact with the box. Although not likely, this can defeat the ground over the years. What is more likely is if there is an insulator between the ears and the receptacle. Then simply remove the insulation. If that grounding conductor is long enough then you can attach it to the green screw of the outlet -- the right way of doing it. If there is not enough wire then an electrician should be called for giving you options if you really need to use that outlet.

@vinylfun 

It is possible what @gs5556 posted above, is possible.

Did you check the other wall outlets in the same room for Open Ground? 

If you have a multi-meter it would be easy to check without removing the outlet from the wall box. You would only need to remove the wall duplex cover plate. Set the meter to AC auto volts. Touch, contact, one test lead probe to the top or bottom of the steel metal outlet box. Insert the other test lead probe in the smaller of the two slots of one of the outlets and check for voltage If no voltage make 100% both probes age making good electrical contact. If still no voltage insert the test lead in the other, longer slot of the two and check for voltage.

If there is a safety equipment ground present you will measure 120V nominal.

Approximate age of the house?

If really old there is a chance the wiring is original and could be old cloth covered rubber insulation. Do not try to remove the outlet. Just pulling the outlet out of the wall box for a look inside could cause the brittle insulation to fall off the wires baring the two conductors.

There is a chance the in wall branch circuit wiring is only two wire. Therein no safety equipment grounding conductor present.

If that is the case, at some point in time the old worn out original 2 wire duplex receptacle was changed out and was replaced with a 3 wire  grounding type outlet.

Use your plug-in circuit tester in the bedroom outlets. What does the tester show? Open Ground?

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Ground"(!)  Without moving everything around to fit the main Power Cable length to a "Grounded" outlet, please is there a safe and best sounding way to still use this outlet to power everything? 

IF there is not any grounded objects within arms length of the equipment and the floor is wood or carpeted there is not a provided path for you to receive an electrical shock through your body. What would you have done if the wall outlet was only a two wire outlet? Used a ground cheater? 

You might want to consider in the near future to hire an electrician and have a new dedicated 20A branch circuit installed for your audio system equipment. 

Also have the electrician check out the Open Ground wall outlet. If it is only a 2 wire circuit, and if the box is deep enough, he can install a GFCI duplex outlet, in place of the 3 wire grounding type outlet. If the box is not deep enough he can buy a new 2 wire duplex receptacle and install it in place of the 3 wire outlet. Or just remove the outlet and install a blank wall plate. 

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Were the faceplate screw in place when you took the reading?

If not install the screw and check it again.

DeKay