I have a built in microwave oven with a broken door open button (the hinge plastic was too thin by design). The plastic is somewhat pliable, waxy. There is no chasing arrow showing the plastic type, but it is marked ">ABS<". In the past I've tried "works on plastic" household glue, PVA glue, super glue and/or plastic epoxy with mixed or worse results. Is there anything that really works on ABS?
The surprising (to me) answer may be ABS cement. You probably won't find this in the hardware store glue isle, instead head over to plumbing:
You'll want the smallest can possible (e.g. 4oz), and after use to seal it in a zipper lock bag and store in a cool dry location. The stuff goes bad in the can pretty fast.
The ABS cement worked for me far better than any of the other glues mentioned above. You can also cut out a small piece of ABS drain pipe, or other ABS item, to use as a patch for the repair.
Note that ABS cement is a mix of a solvent and ABS powder: in the end you really end up welding the plastic more than gluing it. For this reason clamping is recommended.
You can use acetone to glue ABS
We do this a lot with our ABS 3D-prints at our local hackerspace.
According to the lego community, to glue ABS (Legos happen to be made out of ABS plastic as well), you actually want a solvent, not a glue. The solvent loosens up the molecules on the surface of the plastic allowing them to combine, leaving a cleanly fused surface with no residue.
The best choices for solvents to "glue" ABS are MEK or GBL. Although acetone may also work, anecdotal evidence suggests it may take too long or provide a bond that is too weak.
Have you considered welding the plastic? I have a car radio mount that broke when someone stole the radio. I ordered the wrong part from Amazon and ended up having to fixing the mount. Not sure if the plastic was ABS, but PVC cement did not work. In the end, I used a electronics soldering iron and welded the plastic together. Worked great. I have more confidence in the weld than if I would have found a cement that would have worked.