You're best off taking everything down, remeasuring at the new location, and putting the wall back up piece by piece. You'll want to pick the lumber that requires the least cutting to fit in the new location, but if the new location happens to have a higher ceiling (concrete floors aren't level and joists can sag in the middle) then you'll need to get new studs and find another use for the old framing.
To take down the old wall, I'd pull as many nails going from the top plate to the joists above as you can, and then hit the top plate with a sledge to knock the wall over. Use a piece of scrap wood so the sledge doesn't damage the top plate. The studs should easily pull out of the top/bottom plate. If the bottom plate doesn't come up easily, you may want to replace that with a new pressure treated board (you want PT when in contact with concrete). Make sure to use fasteners that are coated to work in PT wood when assembling the wall in the new location.
One final tip, there's nothing wrong with building a wall with two bottom plates. Affix the first bottom plate to the floor, and build the wall for the new location on the ground. When raising the wall, put it slightly over the existing bottom plate until you're completely vertical, and then shift it into place with the trusty sledge. Without the second bottom plate, the wall tends to hit the joists about 6" before you reach vertical. You could also wait to install the second top plate until after the wall has been raised, or stick build the wall in place. But the advantage of the second bottom plate is that all of your studs will be long enough in the new location.