I have recently fixed a common laptop problem where the power button light turns on for few seconds and then automatically turns off.
The problem can be related to electrical/hardware/software.
Most of the cases of this nature is due to failed power adapter. Alaways use original adapter for the subject laptop. The laptop will not start because the battery is empty and the power adpter has stoped providing any power. That is why your laptop is turned on for few seconds.
First of all check power adapter with a multi-meter. Check for loose power connection or faulty power strip.
In some cases you need to remove the battery and switch on the power button with no power cable to dissipate residual charge. Then connect the batter and power source to switch on your laptop.
If you are not able to solve with above methods, go to nearest service center.