I know this is an old question, but I have just had this problem too on my Dell Chromebook 11 (CB1C13). When plugging in the power cord, the light would come on for 1 or 2 seconds then go out again. It would not charge. I tried buying a genuine Dell replacement power supply and it made no difference. I then took the back off, disconnected the charging jack from the motherboard, gave the inside of the jack a good blast with compressed air and put it all back together again. Voila - the laptop is charging again! I can only think that some dust or fluff had got inside the jack, or maybe disconnecting and reseating it reset something.