|So when you connected the monitor with VGA did you get the exact same display? you may need to toggle Fn and F4 a few times in order for it to cycle to the VGA. |
if you get the same broken display on the monitor then indeed your graphics card is damaged. repairing / replacing isnt very easy. if you think you can do it then give it a try,
if the display is clean and normal then its the monitor and or inverter.
From what i have read, resoldering a graphics chip to a motherboard isnt as straight forward as heating it, well it is, but you have to heat it gradually, incramenting the temperature slowly and at a steady pace, you will also need to cover the rest of your motherboard in something like foil to avoid it heating up and burning.
There are always 'best practices' and there are always 'shortcuts' i dont always use best priactice myself, as i am comfortable that i am extrememly careful when i work. but something like this you may want to read about before you go ahead and just heat that sucker up.
read some guides online before you attempt it.