iPod Shuffle (4G) dead, not charging, not detected by PC

My iPod is dead, and whenever I plug it in (original Apple cable, firmly pushed in all the way) the LED glows red for 5 seconds and turns off. My PC does not detect it, and I've tried multiple PCs and USB ports. Resetting does not fix the issue.

What do I do?

If you've tried resetting it as per these instructions from Apple and it still doesn't work, it probably means that the battery is dead. This would be my guess since red light means that the iPod isn't charing:

If a red light is blinking or continuously on, your iPod battery may not be charged.[...]

— http://support.apple.com/kb/ts1412

You should of course, to be extra sure, try charging it with a dedicated charger, that is one that you plug into a socket (instead of the USB port on your computer) to make sure that it's not just a case of the iPod needing more power than an USB port can provide.

here's how I solved the 5-second-light-no-charge issue. You will need some patience though.

Plug your 4th Gen Shuffle into a high-power USB port (preferable the stock wall charger). Wait until the red light goes on and than off. Unplug. Repeat continuously until the light doesn't go off, which means the Shuffle starts charging. It took me about 15 minutes, however it may take longer depending on how low the battery charge is.

Here's a little technical background behind this process. When the device is not being used for a while, especially if it is not charged, the battery voltage falls below a certain threshold becoming insufficient to start the microprocessor any more. However, the processor is necessary to start the charging process, and the device gets into the deadlock. Basically, when you plug it in, it's being charged for only 5 seconds while the red light is on. When you constantly plug it in and out you manually charge the battery in 5-second increments until it's voltage is high enough to start the processor.

I advise to unplug the USB from the charger, not the charger from the socket.