It happens to me with Standalone also. However my data files are stored on my local drive. My error message is 'There was an error starting Zotero' and it won't start. I can access my web version through the browser perfectly.
Help! I run standalone with Chrome plugin on OS X Yosemite. Suddenly I began receiving "There was an error starting Zotero" and the app won't open. I'm storing data on my hard drive, not a network. I searched for the data file, which I couldn't find in the default location, and cannot find anywhere else on the hard drive. I've been searching for "zotero" and "zotero.sqlite." I reinstalled 4.0.29.15 twice, rebooted twice, and still same error message. I can find my data on the web interface, but it's cumbersome and much less efficient. I love the standalone -- it's the most efficient and intuitive reference app I've ever used. Any ideas?
Upgrade Storage
If that doesn't fix it, you could try installing the Zotero 5.0 Beta to see if that helps.
Beyond that, see the steps in Reporting Startup Errors for additional info we'd need.
The recommended step of deleting the Zotero Cache seems to have fixed the problem for me.