Depending on the type of platic you could try to chemically melt it. If its ABS (chances are good for a notebook case) you can put a little bit of acetone on one cracked surface and press them together. The Acetone will dissolve a bit of the plastic and harden again when it evaporates. Just be a bit carefull it will also soften the plastic in the vicinity so you might leave fingerprints in the plastic if not carefull.
If it's not ABS you can check what solvents would be possible to use for the other plastic and if you can get then.
Or use superglue
That's probabpy what I would do :D