What about if you go into the system Settings app, go into Pleco's screen in there, and turn on the option to reset all settings on startup?
If that doesn't help either then I'm afraid the next step would be to delete and reinstall.
Rebooting your entire iPad didn't fix this? Very odd - could you send a screenshot? (take a screenshot by pressing the power and home buttons on your iPad at the same time) Post it here or email to mikelove@pleco.
Restore purchases should be enough to bring back your purchases, no extra ID info needed. Flashcards would only survive if you had them set to sync on iCloud, or if you back them up manually before you delete and reinstall (which sounds like it's not possible here).