Some BIOSes have a 'start up at hh:mm' setting - probably in the power management page. I'm not suggesting you did it - if there is substance to the rootkit idea, that could explain it. If you do find a setting and unset it, then it comes back, I'd suggest a complete wipe & reinstallation and virus check on your data files. Likewise if rkhunter still complains, for safety's sake.
I can't really help with the ATI driver since mine are all Nvidia. Several threads look relevant - try searching for 'ati fglrx cpu black' with all open forums selected.
http://ubuntuforums.org/showpost.php...5&postcount=21 looks interesting.
http://ubuntuforums.org/showthread.php?t=796139 might help.
Also check that the monitor you are using is able to show the max resolution the ATI card is capable of. You could switch the driver from 'fglrx' to 'vesa' to verify that. EDIT: This is silly - I forgot your problem was at logout.
EDIT: BTW, on my system rkhunter's output looks like this:
I think these are ok. See https://bugs.launchpad.net/ubuntu/+s...ter/+bug/86153, bearing in mind that Hardy has added Pulse for sound.
sudo rkhunter --checkall --cronjob --report-warnings-only
Warning: Suspicious file types found in /dev:
Warning: Hidden directory found: /etc/.java
Warning: Hidden directory found: /dev/.static
Warning: Hidden directory found: /dev/.udev
Warning: Hidden directory found: /dev/.initramfs