NOTE: Blinking orange has nothing to do with battery status. Blinking orange is a warning that means DO NOT DISCONNECT (eject iPod before physically disconnecting). The light will always blink orange when connected to iTunes, if the shuffle is set to Manually manage music (or Enable disk use).
However, if you eject the iPod (in iTunes), the light should become solid. Then (if you leave it connected to the computer), it should go from orange to green, when the battery is fully charged.
If the light does not eventually become green, its battery may be worn out. If it's less than one-year old, it may have a defective battery, and that may be covered under the one-year warranty.
To rule out a problem with the USB port, you may want to try shutting down the computer and disconnecting all USB devices (including USB hub), except for standard keyboard and mouse if normally used. Do this to reset the shuffle
Start up the computer and connect the shuffle to a direct USB port on the computer.