Take a small paper clip and hold down the small reset button on the bottom of the unit for ten seconds. Make sure the paper clip is one of the small ones, and is firmly pushing down the reset button. Then plug it into your computer, make sure the green light turns on, and hold down the power button for ten seconds.
If the unit still doesn't turn on, and the unit is within one year of purchase (they were released last Thanksgiving, so yours is still within the warranty) you can call Tom Tom customer support and they will set you up with an RMA - which will be free, but for the shipping to send it to them. They take care of the rest.
Unless you purchased an extended warranty from Best Buy, they won't accept merchandise after 15 days, and even then you have to pay a restocking fee.