Try this if your Dell Chromebook will not power on:

1) Make sure power adapter in connected to electrical outlet
2) Plug in Chromebook - you should see a blinking LED light that is right above power connector
3) After five minutes or so this LED light should stop blinking and turn to a solid amber color
4) Please leave Chromebook connected until light turns off - your Chromebook will now be fully charged. 

This is especially true for the grey model Chromebooks. Similar to most cell phones, when the battery drains completely it may take longer than expected to charge. The manufacturer recommends not letting the battery drop below 6% if possible.