Make sure the docking cable plug is inserted completely into the headphones jack, as shown in this document
http://support.apple.com/kb/TS3572
If it does not connect for power (no light), try pulling it out very slightly to see if you can get the light to come ON.
There are three possibilities for the shuffle not getting power. (1) The USB port not working or not supplying sufficient power. (2) A faulty USB docking cable. And (3) a problem on the shuffle (such as a bad headphones jack or logic board).
For (1), if you are using a USB hub or the spare keyboard port, try connecting it to a direct USB port on the Mac with other USB devices disconnected (you can leave standard keyboard/mouse connected). If you have not shut down (powered off) the Mac in a while, you should do that now (to "reset" the hardware). If the shuffle is still not getting power, connect something else (preferably something similar like a USB flash drive or port-powered external drive) to the same USB port, to confirm it is working and supplying power.
For (2), you'll need to try another docking cable with your shuffle, or try your cable with another shuffle (that is 4th gen or 3rd gen). If that's not possible, and there's an Apple Store nearby, you may want to make a reservation at the store's Genius Bar and take it there.
If you can rule out (1) and (2), the problem is likely to be (3). You said you use it when jogging. It's possible that even if the shuffle does not get wet, over time, moisture from sweat seeps inside the shuffle and causes short circuits.