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thanks all. Wow, I am really disappointed with the Apple Store Mac Techs, especially on the first time I have to use them. I did in an hour and a half what they could not do in 1 full week, Crazy.
 
People in my country (maybe in other countries too, I don't know) use to say:
"If you want something to be done right - do it yourself"
It works for me, at least with computers repair :D
 
Just wanted to update everyone on this. So I suspected after talking to all of you and performing some other test, that it was indeed my graphics card. Well, today I went to the Apple Store and purchased a new ATI Radeon 5770 graphics card for my Mac pro and the Mac Pro boots perfectly. So it was indeed just the graphics card and not the logic board or CPU's like Apple told me. Oh and one other thing. I have a Mid 2006 1st Generation Intel Mac Pro and the card works perfectly. So to all who helped me, Thank you very much. I owe you all a beer..
 
Apple's website says:

Compatibility:

* Requires Mac Pro (Mid 2010) with PCI Express 2.0 slot

Mine is a 1st generation Dual Intel Mac Pro (2006).

Google "baking nvidia 8800" and check out the that option.
 
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