Rebecca

I know my laptop is fully charged and boots up, as the power light is on, but my screen remains black and doesn't turn on....

It sounds like there might be a problem with your audio jack. Be sure to check and see if the sound on your computer is muted or if there is a button on your headphones that could mute the audio. If that is not the solution, then you might need to replace your audio jack. Check the Sony Vaio VPCW21FX troubleshooting page to see if you can find an additional solution there.