The first thing I would do is to pull the charger and the battery out from the laptop. Then I would press the power button and wait for about 30 secs. After that I would try to boot my laptop with only the charger plugged in. So, now when you plug the charger into the jack, you can't see the light blinking and everything remains calm and nothing can be heard from the fan or the hard drive, is that correct?
If is that so and the warranty of your laptop has expired I suggest you to take out the hard drive and try to connect it to another computer through SATA-USB cable. If your hard drive spins up on a different computer and it is recognized there, but cannot power up on your laptop, then the problem is hiding probably in the power supply unit on your motherboard. While on another PC, I suggest you to make a backup of your files just in case.
You could bring your laptop to a technician to make a test of the power connector and/or the power jack center because they might have got damaged.