I bought a home that has a one room addition. The alarm clock in that room was blinking, so I thought the power had gone out.

The rest of the house didn't have any blinking appliances or electronics, so I don't think the rest of the house lost power.

A buzzing sound was coming from an outlet.

When I booted my computer (which was the only thing drawing power), an outlet with nothing plugged into it sparked and killed the power in the room.

I reset the circuit and it looks like at least two outlets got shorted.

Any suggestions would be greatly appreciated.

It could be that the two outlets have loose connections. If a screw is loose to the wiring, it will cause heating, and maybe even sparking. You could turn off the circuit breaker to those outlets, or turn off the entire house breaker, then check to see if the screws are tight to the wiring going to the outlets. If you are not comfortable doing this, see if someone else can check it for you. The outlets themselves might also be bad. Good luck.

Thank you! I'll check.