I installed F13 on an old laptop (Toshiba L35-S2174). The CD passed an integrity check and did not give me issues when in the LiveCD environment.
After the install and last configuration, I logged in and went about getting updates and exploring. About 5 minutes in Xorg apparently locks up and starts shifting between different colors (hence "rainbow") as it slowly fades to white.
I figured it might be an Xorg misconfiguration (there wasn't an xorg.conf) so I went and created one with a configuration the I know that works (I have had a few other distros on here for testing, none have had this issue). This did not resolve anything.
I will attempt to get a hold of log-files for Xorg and whatever else you may need.