I would try:
1. If you already had an existing Dropbox account, log in to the Dropbox website, go to Settings, My Apps, and delete YNAB. This will force YNAB to try to reconnect to Dropbox and, perhaps, download successfully.
2. If you didn't already have Dropbox or #1 didn't work, try uninstalling YNAB, installing the Dropbox app for the device, and reinstalling YNAB. If this works, you can delete the Dropbox app if you want.
If those don't work, I'd contact support directly.