This plug in th e basement has no power when I used my tester it showed no lights on.. so it has four wires 2 black 2 white how do I connect them to have power and out of all the plugs in the basement in the room it's the only one with no power

Test between the black and the white wires, if they have no power it explains why the outlet is dead, the whole run is dead. One or both of those blacks should be hot 24/7, back to you

Do you have a GCFI in the basement as well.
Check that too.

There is a gcfi and its in the bathroom in the basement as well but it shows that ground when I use to test it the ground light turns on so I don't know... but none of the wires have power so what do I do..

Sometimes the GCFI will protect other outlets after it. I was asking about this, just to see if that may have been tripped. If that outlet works, then your power problem wouldn't be caused by that directly.