Hi There !!
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It's could be because of two reasons.
1. The Laptop is Overheated
2. The battery of the Laptop has some problems.
To diagnose this:
Step 1: Let the computer, be turned off for 15-30 minutes. Unplug the battery, Unplug any external Hardware connected to the laptop. Could be any external drive or any thing.
Step 2: After 30 minutes of disassembling the laptop. Let's put the battery back in & don' plug the power chord. Just give it a try to turn it on without plugging it in to the power jack.
Step 3: Still no joy, Try to plug the power chord back again & try to adjust it. Because Power port detects the power cord
only after much adjusting of the cord and putting a weight
on top of the cord so that the cord somehow makes c
ontact with the power port
on the laptop.
This is really the case with Vaio & Acer laptop because of their complex design.
Step 4: Check the voltage of your CMOS battery. if your battery is low it will fail to power up the system. if you leave it sit for a l
ong period of time, it may be having a chance to "recharge" itself. This step should be done by a professional, because you might damage other part of the machine .
If your computer in warranty, Call Vaio Helpline right know. And, if any chance your computer is little old dont call Vaio help line because they charge heavily. Contact the local tech shop, even for your reference
http://www.compusa.com/ it's cheap & good service dealer for laptop.
Hope this'll direct you in the right direction.