X not Load!

What hardware does the machine have? Specifically the graphics card.
According to the log, you are trying to use the wrong driver (ati) and it's falling back to the default (vesa) driver. It's selecting a resolution of 1024x768, and X is loading correctly. Then you close out of X, and it closes the log file successfully.

Go to the page SirDice linked, and read through the section for Kernel Driver. You need to load the KMS driver first. Then edit your xorg.conf to use the radeon driver (or just delete that file completely and let the system auto-detect everything).

Then, hopefully, everything should work for you.