That software bundle disk is exactly how my daughter got her Photoshop Elements 3 originally (with a Wacom tablet, still in use). It was originally installed on the old iMac G5 PPC (10.5.8) I still use from time to time (like right now), and has survived being migrated to an iMac Intel C2D (upgraded to 10.6.8) 4 years later followed by migration to the Macbook Air (10.6.8). Which is why I am perplexed about your experience, but maybe something is different about Element 4 versus 3. [But we also have Elements 6 similarly migrated on all these machines as well.] We actually have purchased separate copies of Elements 3 and 6 over the years due to having it on multiple machines. Right now, both version are running on 3 machines under 10.6.8, so I think yours should work also! We need to find out how.
To figure out if this a problem with the computer-wide installation or rather a local user-specific problem, try running the program from another user. If you have only one user, please create a new one and then try Photoshop Elements.
If the problem is user-specific (works for users except for one user), then I suggest you move the following three files out of that user's Preferences folder to a safe location, restart, then try the program again:
Photoshop Elements 3.0 Settings (a folder)
Photoshop Elements 3.0 Paths (a folder)
com.adobe.Photoshop.Elements.plist (a file)
If the program works, then trash those files/folders that you moved and you are done. If the program still does not work for that user only, some more detective work may be needed.
As for the case where the program won't work for ANY user, you may need to consider reinstalling the software. For that, it is best to uninstall it first, if you have an uninstaller on your install disk (the software bundle disk). If not, one needs to search for and remove all signs of the software (the above files, the software package itself in the Applications folder, etc.). Then reinstall.
If all else fails and you have gotten tired of this, you can purchase a much newer version of Photoshop Elements (version 10, I think) that is much more capable and has been recently adapted for newer computers and operating systems. Probably ~ $100 or so. But I wouldn't give up yet.