Is there a way to recognise an ipod shuffle that is unresponsive?

Which model is this shuffle? This document shows the four types

http://support.apple.com/kb/ht1719

If it's 2nd gen, you need to use the USB cable it originally came with (it has a mini-dock on the iPod end), or a compatible third-party replacement. The USB cable for the 3rd and 4th gen shuffle fits, but does not work, because the connector is different.

Did this shuffle work with this computer before (with the same OS and iTunes installation), and does not now for some reason? Or are you trying to connect this shuffle to this computer for the first time?

There are three possible causes. Problem with USB port, faulty USB cable, and problem on shuffle.

To rule out a problem with USB port, shut down (power off) your computer and disconnect all USB devices, including hub, except for standard keyboard and mouse (if normally used). If your computer is a laptop, connect its power adapter (so that it's not running on battery power). Do this to reset your shuffle

http://support.apple.com/kb/HT1655

Start up computer, run iTunes, and connect shuffle to a direct USB port on computer. When you connect it, note if the shuffle's light comes ON in any way. If there is no reaction on the shuffle or computer, connect something else to the same USB port, to confirm it's working (preferably something similar like a USB flash drive or external drive).

If that does not help, to rule out a faulty USB cable, you'll need to try another cable, or try your cable with another shuffle. If that's not possible with what you have, if there is an Apple Store nearby, you may want to make a reservation for the store's Genius Bar, and take it there along with your USB cable.

If you can rule out USB port and USB cable, the cause is probably a hardware problem on the shuffle. If you do not see the shuffle's light come ON in any way when you connect it, I would suspect the fault to be in the headphones jack or the logic board.