We have 2 bedrooms on the same circuit and there are problems in one room.
My son has things plugged into a ups and sometimes it will start beeping. Nothing new plugged in, it just starts and its sporadic. It was suggested the outlets be checked to see if anything is loose. An electrician is not in our budget right now. Is that something we can (or should) do? The other bedroom has no signs of any problems.
The best remedy would be to install a new plug, as Steve mentioned above kill the power at the breaker and check that it is out with a volt meter or basic circuit tester...the tester is pretty cheap and can be purchased at the home center when you pick up a few outlets ( get a few and upgrade those that seem "loose" when something is plugged in) use the screws on the sides not the back stab.
Let us know how it comes out...BTW the plugs are pretty cheap you can get really good ones for about $2 ea....stay away form the basic .69 to .99 cent ones.