There are 2 approaches you can take. One of them is installing the system as a fresh install by running the OS X Leopard Installer again and selecting the Archive and Install option. This option is available after the Select a destination screen.

Doing this will install an entirely new copy of the OS and will move your existing Mac OS X system files to a folder named Previous System. Choose the Preserve Users and Network Settings option to archive user accounts and their home folders.

A second solution is available to try if you are familiar with using Terminal. This solution can help remedy problems caused by third party software references that are not compatible with Leopard. The following steps will remove these references:

1. Start the Mac while holding Command-S after restarting the computer.

2. Type these commands and press Enter after each one is typed (be careful):

/sbin/fsck -fy
/sbin/mount -uw /
rm -rf /System/Library/SystemConfiguration/ApplicationEnhancer.bundle

3. Restart your Mac.

See also:
Mac OS X 10.5: “Blue screen” appears after installing Leopard and restarting