You can absolutely fix pressboard furniture! I have done it many times. The key is that you have to accept it will never come apart again!
Use Gorilla Glue or something similar and clamp it down or weigh it down tight for at least 24 hours. You may need to carefully clean up some of the glue after it dries (it expands).
In order to fix it properly, be prepared to take it apart - at least part way. While you are at it, add some glue (Gorilla or wood glue) to all of the joints. Even with the screws and bolts, etc.
Good luck!