Delicious Library 3
A few thoughts.
From a quick review of the Delicious Library webpage, OS X 10.4.x Tiger compatibility doesn't seem to be an issue, so I think it's best to look in other directions first.
Have you tried trashing the preference files associated with the applicatioin, then restarting? The filenames will probably contain the app's name, and end with .plist. (Look with ⌘ - F > Name.) If you're not familiar with this procedure, you can read about it in KnowledgeBase article 301084: Mac OS X 10.4: Reopening an application after it unexpectedly quits.
Have you repaired permissions lately? (See Article 106712: Troubleshooting permissions issues in Mac OS X and Article 25751: About Disk Utility's Repair Disk Permissions feature.)
If the app is actually 'crashing' i.e., 'quitting unexpectedly' an error report may have been generated that could provide information about what's awry. Here's one place to look: Open Console (it's in /Applications/Utilities), click on the 'Logs' icon at the top left-hand corner, and click the gray 'disclosure triangles' under it next to ~/Library/Logs and next to CrashReporter within that. Hopefully, there'll be something like DeliciousLibrary.crash.log there. Double-click it to open, copy the relevant sections of the log that comes up in the right-hand pane, and paste it into another post. One of the UNIX-experienced folks here may be able to help you interpret what it says.
I hope one of these suggestions is helpful.
Cheers!
Dean
Delicious Library 3 Review

Delicious Library allows you to categorize pretty much your entire life and keep a running inventory of virtually anything you own. This can include books, movies, music, games, gadgets, and more. With built-in Amazon support, you can find virtually anything to add to your library or just scan bar codes in order to add items. Friends that use Delicious Library can view your library.
Sep 30, 2005 4:15 AM
Delicious Library 3 Review
Delicious Library 3.3 has been redesigned for OS X 10.10 “Yosemite”—it's now the hootinest tootinest shootinest library program in the west! In fact, this build ONLY runs on Yosemite. (Don't fret if you have 10.8 or 10.9—it's a free upgrade to 10.10, and your machine can handle it.). Delicious Library 3 has a strong philosophy behind this design, and it’s nice to see that designers and developers feel strong about it. It is a clear upgrade from the previous version since interface is shinier and it now comes with some amazing animations. Delicious Library has not become entirely unusable, but it’s definitely taken a huge step back in usability. I waited for a few months, hoping that these issues would be addressed in subsequent DL 3 updates, but there have been many updates now, and most of the issues I describe here are still there. Delicious Library helps you create a comprehensive inventory, share it with friends, and get holistic recommendations based on your collector profile. Scanning is easy: simply hold barcodes up to your webcam, and items appears on your digital shelves in gorgeous 3D.
