Garmin GPS devices, as with any other electronic device, are prone to malfunction. A Garmin may not power up even when it is plugged in for several reasons. The issue may be power, the device's battery or a software or firmware malfunction. Usually these issues can be fixed without having to return the device to the manufacturer.
Charge the Garmin with a different power outlet. It is possible that the charging outlet is not providing any charge. Try charging the Garmin in a different vehicle or power outlet.
Make sure the temperature is within a range conducive to charging. Many Garmin devices, such as the Nuvi, will not charge properly in temperates below 32 degrees and above 113 degrees Fahrenheit. It also may fail to charge properly if placed in direct sunlight.
Reset the Garmin if it appears frozen. Often the device can be reset by turning it on and off. You can also slide the Power key to the left and hold for at least eight seconds. If the Power key doesn't slide on your Garmin, hold the Power key down to trigger a reset. Then release it and it should unfreeze itself.