What you are experiencing are kernel panics. These are usually the sign of hardware problems or corrupted software.
Do you have any third-party RAM in the computer?
Do you have any USB or FireWire devices attached to the computer?
Have you installed any third-party software recently, especially anything with drivers such as multi-button mice?
Try starting with the Shift key down to turn off extensions.
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Sounds like a kernel panic :-x.
Try booting into safe mode as seen here:
then you could try and repair your disk permissions in disk utility under the utilities folder in your application folder.
try that and then get back to us .
Usually means the system is hosed. You may try this:
How to Perform an Archive and Install
1. Be sure to use Disk Utility first to repair the disk before performing the Archive and Install.
Repairing the Hard Drive and Permissions
Boot from your OS X Installer disc. After the installer loads select your language and click on the Continue button. When the menu bar appears select Disk Utility from the Installer menu (Utilities menu for Tiger.) After DU loads select your hard drive entry (mfgr.'s ID and drive size) from the the left side list. In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive. If it does not say "Verified" then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is "Verified" then select your OS X volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported, then quit DU and return to the installer.
If DU reports errors it cannot fix, then you will need Disk Warrior (4.0 for Tiger) and/or TechTool Pro (4.5.2 for Tiger) to repair the drive. If you don't have either of them or if neither of them can fix the drive, then you will need to reformat the drive and reinstall OS X.
2. Do not proceed with an Archive and Install if DU reports errors it cannot fix. In that case use Disk Warrior and/or TechTool Pro to repair the hard drive. If neither can repair the drive, then you will have to erase the drive and reinstall from scratch.
3. Boot from your OS X Installer disc. After the installer loads select your language and click on the Continue button. When you reach the screen to select a destination drive click once on the destination drive then click on the Option button. Select the Archive and Install option. You have an option to preserve users and network preferences. Only select this option if you are sure you have no corrupted files in your user accounts. Otherwise leave this option unchecked. Click on the OK button and continue with the OS X Installation.
4. Upon completion of the Archive and Install you will have a Previous System Folder in the root directory. You should retain the PSF until you are sure you do not need to manually transfer any items from the PSF to your newly installed system.
5. After moving any items you want to keep from the PSF you should delete it. You can back it up if you prefer, but you must delete it from the hard drive.
6. You can now download a Combo Updater directly from Apple's download site to update your new system to the desired version as well as install any security or other updates. You can also do this using Software Update.
Note that if the hard drive is not OK and cannot be repaired, then you will have to reformat the drive and reinstall OS X from scratch.
If you don't have sufficient space you can omit the language localization files, Asian fonts, and any printer driver families you don't need, but you should install the family for your printers unless you there's not driver for your printer in OS X. Here's the guide to included drivers: Printer drivers included with Mac OS X.
If you can it would be a good idea to backup your personal data files, iTunes library, etc. to an external drive so you can delete them from the system volume until after you finish the Archive and Install. This will free up more disk space.