Hi John, cloning is a great clue, I suspect you have something incompatable running in the Background...
Open Activity Monitor, Show:>All Processes, sort on CPU%, see if anything using too much CPU% when this happens.
Open Console in Applications>Utilities & see if there are any clues or repeating messages when this happens.
One way to test is to Safe Boot from the HD, (holding Shift key down at bootup), run Disk Utility in Applications>Utilities, then highlight your drive, click on Repair Permissions, Test for problem in Safe Mode...
PS. Safe boot may stay on the gray radian for a long time, let it go, it's trying to repair the Hard Drive
Reboot, test again.
If it only does it in Regular Boot, then it could be some hardware problem like Video card, (Quartz is turned off in Safe Mode), or Airport, or some USB or Firewire device, or 3rd party add-on, Check System Preferences>Accounts (Users & Groups in later OSX versions)>Login Items window to see if it or something relevant is listed.
Check the System Preferences>Other Row, for 3rd party Pref Panes.
Also look in these if they exist, some are invisible...
Another clue, the computer thinks that its name is "Kathy's Mac Book Pro 2" and I have not figured out how to change it.
BDAqua's advice is good. I agree that you are probably looking at needing a clean installation.
On the simpler question above, you should be able to change the computer's name in System Preferences>Sharing.