Electricians and The Like: Help!

If you shut off all of the breakers and the computer never went off, then there is another box somewhere. Or you have a UPS.

I think what Rhubarb wrote sounds likely. Something else worth keeping in mind given the age of your house is that it could have aluminum wiring. This is fine as long as the receptacles are rated for aluminum wiring. What you find in some older houses is that the receptacles have been replaced at some point with copper-rated receptacles and the connections heat up when a (relatively) high current device is attached. An electrician will usually know to look for this, your maintenance man might not if he decides to fix it himself. It’s a huge fire hazard so you should be aware of it.

I never suggested an outlet be dismantled.

That was a new thought. Only the first sentence was for you. I should have separated the two thoughts better.

You could also have an open neutral somewhere on that circuit and that could be upsetting to any electronics you may plug in. Make sure to use a surge-suppressor on that tv no matter what you find.
I third or fourth calling the LL. You don’t want to monkey with old wiring. It can be a bitch, seriously.