Try removing the battery and plugging in the power supply only, if that doesn't work remove the batter and unplug the power supply, press the power button then leave the computer over night. Plug it in the next day and see if it works.
Sounds like voodoo but I have tried this on a few laptops and it worked. If none of these tips work then the power supply is probably bad. Either get it tested or get a new one. Worst case scenario, if the new power supply doesn't work then the motherboard is faulty.