these white imacs are known for this graphics failure
they are also known to be able to be upgraded by swapping the cpu for a T7200, T7400, or T7600 socket M laptop cpu which upgrades it to a full "Core 2 duo" 64bit capable machine
u will want to check the adapter in the specs to make sure, but im pretty sure its a mini DVI port that u want to get
i have one for my imac 2008 i believe its the same
b
1st step: get teh adapter
and try to plug it in so u can find out if it works
depending on whether or not its the screen thats blown or the video card itself
u may be in business.. on the other hand it might be a good thing that its the video that is blown and not the screen.. u could replace the graphics unit
by opening the imac if u went that far to do al that work u might as well go ahead + upgrade the hard drive inside to ssd etc while u have it open coz its a pain in the ass to open - u can find videos online on how to do it using a plunger or suction cup device to pop off the screen - its easier then u think but would require some skill, Effort + patience + determination thats for sure
on the other hand for the same cost as the repairs u may find another white 2006 imac for the same price u can pick these up for about 200 bucks in my area in classified ads