Slide the power switch to the On position, and hold it there for 10-15 seconds. This will perform a soft reset of the device. In fact, if you have headphones on, you can actually hear teh soft “click” as the device resets.
Then, try powering up as usual, with a brief press to the On position.
If the device is recognized by the computer, and is communicating, be sure that it’s charging. Have a look at the charge indicator. Is the battery charging, and does it show a charge level?
Better yet, if you are in MTP mode, open a Windows Explorer window by pressing [Windows Key] = E, or go to My Computer. With the Clip connected, right click on the device and select Properties. Check that the battery is charged. In MTP mode, you can see the charge level.
If this is OK, and the Clip suddenly dies when disconnected, you may have a bad battery or connection internally. Contact Support at 1-866-SANDISK for further assistance.