Some adaptors are noisier than others, in my experience (which amounts to about half a dozen!)
I assume the battery is dead, as you mention the problem is one of the laptop not powering up with or without the battery. I had a Fujitsu battery fail after 18months but it ran on the adaptor OK without the battery fitted.
One of my 2 Dell adapters makes a buzzing sound when it is on, but it is not noticeable if it is on the floor when I am working.
A longshot - try connecting a monitor and see if you get anywhere. One of my Dells only powers up if an external monitor is connected. It did exactly the same as yours - HD started, lights flashed on then nothing, it works perfectly with a monitor plugged in. I think it must be something to do with the screen.
It is limiting though, considering a laptop is supposed to be portable.
Good luck with the fault finding.