I build flat pack furniture for a living and see many disasters like this. It is actually fairly easy to a) avoid and b) rescue.
If you don't put the back on, it is basically just like a card box without the base and has no lateral strength whatsoever.
The first thing to do is avoid it and that means build the wardrobe lying down on the cardboard packaging on its front. Then put the back on before you lift it. If you cannot do this, position one vertical piece against the wall so it doesn't fall or get a second person to hold it. Attach the base and two supports, then attach the back panel. This will form a rigid corner and then you can add the remaining side and top to the wardrobe. It requires care but can be done easily.
If you have made a mess of it, all is not lost. Both sides are universal and the top fixes to the top row of holes and the base to the third row of holes. If you have ripped the torsion pins out of here, simple swap the sides over and you can have a second chance to build the wardrobe.
In terms of repair, before your second attempt, gently knock the chipboard back with a hammer. This is often sufficient and it compacts quite neatly or you can use furniture wax.
I hope the above info is useful.
For plenty more tips and trick just visit my website, Flat Pack Advice.