Sony Vaio FW - completely dead?

Uhmm if you hear a 'buzz' then there is a electrical discharge (short) somewhere on the Mobo and the Mobo is DOA. You can salvage the RAM and HDD, depending on the model (older RAM wont' work on newer laptops, and if the HDD is a standard 5400RPM then isn't worth keeping with how cheap new HDDs are) but yeah toss the lappy.

You shouldn't hear any buzz, a buzz is normally electricity or a ultra quiet fan. But your stating nothing is getting powered. If you took out the battery and just worked off wall power (like a desktop) your still not getting anything. So these repeated steps all prove, yes this is a dead system and needs to be replaced.

Hi, verify the voltage coming out of the adapter, it's written on the adapter itself. After we will see.

You said you took out the power jack, do you have four wires from the jack to the motherboard, and at the jack, what voltage do you read?

You can verify something, take out the motherboard, connect the adapter and try to find where the buzzing sound is coming from. Maybe you will find the defective part, who knows.

I could help you if I find the schematics, what model do you have? And for the noise, if you touch the parts with your finger, maybe you will sense some vibrations.

I can't find any informations, no schematics, no service guide. It's difficult to find informations about Sony laptops. Sorry, you need to replace the motherboard.

Your power input port might be broken, a know issue with the FW series.
Happened to mine when it got dropped and the small plastic centre piece broke off

@RangerCoaster...did you finally find some solution. I am facing the exact same problem with my sony vaio. No sighn of life just a very very low buzz...

ANSWER: You need to buy a new laptop. If there is no 'high end needs' then a simple $249 one at Walmart is all you need for you. Otherwise buying something more powerful will be very costly depending on the 'needs' you want from it to perform.

FINALLY. FOUND PROBLEM and SOLUTION. Successfully broght it back to life (twice). Here is my story.

I was using Ubuntu. The battery care feature in sony was the main culprit. Its buggy. Its value was somehow automatically taken to 0 by the system and it refuses to start. If its value is reset to 100 somehow, the machine becomes stable. But the main challenge is how to set its value in a dead machine.

Heads up! you need to be really patient in the process and the process needs to be done in a quiet place. By enourmous amount of fiddling, here is what I did to start the machine.

1. Removed the battery. Plugged in the power chord.
2. Listen to the buzz carefully. Pressed power button for 1-3 seconds and released, repeated the 1-3 seconds press and release for many times observing the buzz sound. If there is some disruption in the buzz sound, chances of machine bootup is high. Kept pressing intermittently while the buzz disrupt (every half seconds or so), machine started but again dead in couple of seconds. Kept trying and after some boot and dead, It gave me enough time to change the battery care limit.
3. Once its started temporarily, opened terminal, edited "/sys/devices/platform/sony-laptop/battery_care_limiter" with 100, saved and rebooted.
4. Machine restored. For future, I have removed Ubuntu and now I am relying on windows. I hope it doesn't happen in windows as it didn't for more than a year.