Is the latest iTunes installed on the computers? If not, you can get it here
http://www.apple.com/itunes/
An older version of iTunes, depending on how old, may not support recent iPods.
Make sure the shuffle is fully connected to the USB cable (plug is fully inserted). The fit may be tighter than expected. It should "click" into place.
This is a new shuffle, so it's 4th gen. The are both 4th gen? It comes with a short USB cable. Those are the two cables you tried (one from each of the two shuffles), correct? If so, you can probably rule out faulty cable as the cause.
Since you tried multiple computers, and multiple USB ports, you can probably rule out faulty USB port as the cause. To be sure, it would be a good idea to shut down (power off) and disconnect all USB devices including hub (except keyboard/mouse if normally used) on one of the computers, and connect only the shuffle to a direct USB port on the computer.
Since you have two shuffles to try, if they are both new (or recent), it seems unlikely that you would get two with hardware problems.
If the above does not help, I think the most likely cause is a software-related issue on the computer, but it seems less likely because you tried three (unless all three of the computers you tried are configured similarly).