Try starting the third GPU first.   If it works fine, than it is probably a problem caused by the PSU.

I have some watercooled 5970s.  I still have the reference air coolers, they do not have many miles on them because they were only used for gaming.  I am travelling for work, but when I get home this weekend I will post them for sale in the classifieds.  I had no clue there was a market for them.

I have 6 of them.

3x Sapphire
1x XFX
1x Powercolor
1x Diamond

I have been lurking for about a month.  This post made me register so I could post.