Logic board need replacement?

I'm troubleshooting for my parents' iMac.

Part # MC413LL

Model# A1311 (last four digits of the serial #zb9u)

It has all it's original parts (although are unsure, the logic board might have been replaced while still under warranty), it has been into 'the shop' a couple of times because of viruses and to have security software installed and/or updated.

This time they took it in because 'it wouldn't boot and the picture was all funny'. They were quoted $900+ to fix it, so they brought it home.

When powering on, the screen is pinkish and pixelated (small rectangular, horizontal blocks of colour), the Apple shows up kind of in a grey square and you can somewhat see the circle spinning below. The entire screen goes white/light grey then blue. If booted in verbose mode, it's hard to read as the small coloured rectangles still show over the white text on black background, however it will do one more step beyond the blue screen to half purple, have black blocked out in small white squares.

I tried hooking it up to an external monitor, but it shows the same starting with the white/light grey screen, so assuming it's not a graphics issue.

It looks like there are no logic boards for sale for it on here, I checked another site quickly and saw one for $600 and another for $1500. At those prices they'd rather replace the entire computer. I read somewhere though that it could be as simple as swapping out a couple of blown capacitors. Any thoughts?

Before they rush out to purchase a new computer, is there any thing else that it could be?