Electric outlet only has 2 wires and no power, how to replace?
What you need is a wire tracer.  There are two types: one for live wires, the other for dead wires.  Your local tool lending library may be able to help.

It's quite possible you won't find the other end of the wire, or that it was disconnected in some other renovation.  It might drop into the basement, or head in some crazy direction.

And while K&amp;T is good stuff:
https://diy.stackexchange.com/a/20279/5960
this one may not be worth saving.  At a minimum you'd want to put new shrink wrap on the wires through the metal box, and use emery paper to brighten up the copper.  Then put a two prong outlet in.