If you have not already, try more than one USB port. Also, shut down (completely power off) the iMac, then start it up. Do this iPod shuffle reset procedure and try connecting it again.
http://support.apple.com/kb/HT1655
Unfortunately, if this is a first gen iPod shuffle (white color - looks like a USB flash drive), the weakest part seems to the USB connector. Just for "fun," a few years ago, I bought a bunch of first gen iPod shuffles on eBay that were described as "broken." I wanted to see if I could swap parts to make some good ones.
The most common failure was to the USB connector. I guess it just wears out from repeatedly being inserted into USB ports over the years. If the USB connector is bad, you can't do anything else to try to make it work (such as a Restore in iTunes), because there is no connection.
Try connecting the iPod shuffle when iTunes is NOT running. Does it get recognized as a disk by the system in any way? For example, on a Mac, it might appear in Disk Utility or a Finder window. If it is recognized in some way as being connected, that's good. You might be able to use the iPod Reset Utility
http://support.apple.com/kb/HT1238
It's supposed to do a reset at a lower level than a Restore in iTunes. But if the iPod shuffle is not recognized because the USB connector is bad, it won't help.
