Hi...
My laptop shuts down whenever I connect to the internet,try to download songs,watch movies or even play games...
Do you know why it happens??
My laptop is a lenovo Y500... it has 1 gb ram and 80 gb hard disk

Have you checked the battery. Go to control panel and click on power options. Also, in Control panel click on Internet options , click on screen saver , then Power. Adjust the timer longer before shut down.
Another possibility check if cooling fan is running, over heating can shut down your computer. They make a aux cooling base for laptops, it has a extra fan that runs off USB port. Only around 15 -20 $ Especially if you set it on bed or couch it can interfear with vents on bottom of laptop. If you have not cleaned out inside computer it can cause overheating.
Hope this helps.
hawk_eye

First take out the battery then, remove main power supply and Press or hold the power button down for a minute. After that put the power supply but don't put the battery and turn on your laptop and now put in battery.
Or if still same then recommended that you should scan your computer with effective anti virus.