Are you sure these applications came from the correct operating system disc? Macs can only boot the operating system that shipped with them, and newer retail operating systems. You may have installed a version too old or too new. You may also need to repair permissions. Also if you installed any cache cleaning software, that can affect Apple applications ability to launch. Remove that kind of software.
I booted from the Snow Leopard retail installation disk, used Disk Utility to wipe the hard drive and then Time Machine to restore the disk. The applications did not work after the restore.
Based on another post that seemed to have this problem, I then ran the installation for the applications from the same Snow Leopard retail installation disk. Still does not work.
I checked other programs and found that the iWork and iLife applications also were not working, but other company's applications seemed to be working.
I can check permissions, but this seems like a long shot. Why would the permission on just Apple programs get messed up by a restore and not other software?
I do not use any cache cleaning software.
Any other suggestions?
Seems to me your TimeMachine drive is messed up somehow. Disconnect it
Copy your users file folders (Music, Docs etc, not Library) to a regualr external drive, export any bookmarks, product license keys or any data (program names) you require to rebuild the machine from scratch with. Write down your User name, case sensitive. Disconnect.
Hold c boot off the 10.6 installer disk, use Disk Utilities under the Installer menu to Erase > Security Option > Zero All Data the ENTIRE boot drive, it's on the far left with the drive makers name and size.
Let this complete, it's going to take some time to finish and really scrubs the drive, makes sure all the bits are working.
Next install 10.6 and reboot, setup with the same name as before and use Sofware Update to get the machine on 10.6.8
Next, install your programs from original sources, (like from the 10.6 disk) as many as you possibly can, they will run faster if they are installed before your huge files. This is also you get a nice clean copy free of issues.
Last, hook up your external drive (not TimeMachine) and return the contents of Music to Musc, Doc's to Doc's and so on into the same named user account folders.
If you keep your boot drive below 50% filled, it will operate very fast forever, just don't move it while it's running. The Zero Erase hopefully fixed any bad or damaged sectors on the boot drive that might be the reason for your problem, or it might not have been, I don't know.
Once you have a yourself a nice and clean fresh install, take this moment to erase the external drive (no data) and use Carbon Copy Cloner (free) to clone your internal boot drive to the external drive.
You can hold the option key and boot from this drive at anytime, setup CCC to auto-update the clone as a backup.
You can access the files on the clone drive too, just like any other drive.
Far as TimeMachine, you can still use that, do the same Zero Erase on it and set it up again.
What I suspect happened is something corrupted your data on the TM drive and thus when you restored it was corrupted. Bad sectors on hard drives can do this.
I can buy that there are may be bad sectors on the hard drive, but, the chance of the bad sectors only affecting Apple applications is not credible. Again, all the other applications that I have tried seem to work, it is only Apple's programs that are not.
I did repair the permissions as suggested above, and that did not help.
Why would only Apple's programs fail to launch? And how can I reinstall these applications?
You hsve a tough one here. Since you aren't using any cache cleaning software, and permisssions are not at issue, the CoreServices files themselves must be damaged either from the source or in transit when being installed with the operating system. Either way either replacing the installer disk or the hard drive may be neceessary to resolve this issue. And if neither works, then the optical drive itself might be dirty at just the wrong location and needs to be cleaned. Also bad RAM can behave this way and not show up on any hardware tesr. Regardless an erase and install of an operating system disk that is supported, can only mean one thing if isn't running right...a hardware issue.