Unhappy System / User apps dissapearing after force shut down during boot.

My cheap, $100NZD qm734g Tablet started crapping out after I had to hold down the power button during boot...
Apps (including but not limited to; Google Play Store, Clash of Clans, Hay Day, Google Services and several other app's app data / cache) have disappeared from the list of installed apps, and the app manager. Au though, they seem to still be installed, all the files in /sdcard/Android/Data and /sdcard/Android/obb are still there (I think it's the same deal on internal storage, too...) but the entry from the App launcher is gone.

It is rooted, but only after this first started happening, as an attempt to fix it.
I have formatted and returned Android to factory default, (Power Button + Vol Up didn't work for some reason.) but the same issue relapsed after 2 days. And now Google Play (com.android.vending) is missing...

I doubt there isn't much I can do that doesn't involve flashing a new image, but if that is the case, Clockwork mod and Cyanogenmod aren't compatible, so I'll need some help there, too...