I have an advent monza c1, my son stood on it and it wouldnt start. i thought the motherboard was broken but iused a hdmi cable to connect to my television and it works.
i took the laptop apart and put it back together again, now two thirds of the screen works perfectly but one third of the screen is just white.
Do you think this is the inverter or a damaged screen?.

This is not inverter related failure, that’s for sure. You still can see part of the screen, it means the inverter works properly.
Your description sounds more like LCD screen failure. I would try replacing the screen.

One of my laptop Dell Inspiron 6000 is having problems. When i boot the machine the screen is on just for 5 seconds and is more like red/pinkish, after that is black. If i look closer i can see that the LCD is working but there’s no light. What could be wrong?

Sounds like backlight lamp failure. The backlight lamp is mounted inside the LCD screen and very hard to replaced.
When backlight fails, I suggest replacing the whole LCD screen.
This guide explains how to replace LCD screen in Dell Inspiron 6000 laptop.
Here’s one suggestion. If you decide to replace the LCD screen, buy one which comes with inverter board installed.
If you install a wrong screen (not compatible with the inverter) the brightness will not work properly.
I found that with Dells it’s always better to replace LCD screen with inverter together.

I bought a replacement screen for my vaio vgn fw and i managed to replace it, but, I have a question, the video cable should go all the way in? My video cable is taped to the screen, should it go all the way in in the screen socket or just touch the socket?

The video cable has to be plugged into the socket, not just touch the socket. Why are you asking? You cannot plug it all the way into the socket?
Take a closer look into the socket on the LCD screen. Does it have a row of very thin pins? Make sure there are no bent pins inside the socket on our new screen.
Again, the video cable connector has to be plugged in.