Is my kitchen cabinet door beyond repair?
Plan A) I'd try to remove the glue, fill the holes†, let it set and then re-drill the holes 

Plan B) Use repair plates designed for this job Example

Plan C) If all fails I'd spend $10 on one of these, put it in my old electric drill's chuck and relocate the hinges.



† Using maybe something like an "Interior Wood Filler that holds screws and nails".