Does the fridge make any unusual noises, like knocking or gurgling perhaps?
When you turn a fridge upside down and keep it like that for a long time, a couple of things can happen, some worse that the others. The oil from the compressor could have flown into the refrigerant lines and is now clogging it. It may not be a permanent thing though - let it sit unplugged longer (24hrs+). With any luck it will run back down to the compressor and free the line. Unfortunately, it can happen again in the future if there's any oil left in the lines.
Also, the design of the fridge does not really allow for upside down handling (especially moving) because the mounting hardware of all heavy parts is designed to work only one way - prevent the part from crushing down. Once you turn it upside down, it's no longer strong enough to prevent (or damper) movement and the heavy compressor can damage the line tube connections and the refrigerant can now be all gone. Does the compressor run constantly? This may be the sign. It's a permanent problem, won't fix itself, you'll need a technician's visit.
Another thing, too: if you don't hear any unusual sounds, and the condenser on the back is warm, let the fridge run for several hours. It may actually take up 48 hours or longer for it to eventually reach the normal cold temperature. It would be rather unusual for a brand new fridge, but from the question I could not tell for sure if you're talking about a brand new fridge or it's your old fridge moved to a new home while upside-down in the mover's truck.
So, the plan should be to let it sit longer still and if it does not start cooling, call a repair technician. Â