Can I melt or weld broken ABS plastic back together?
Back in my University days I worked at a place that used to modify vending machines to allow 12oz cans to be vended in 16oz machines. They did this by adding ABS blocks to the racks using a very liquid substance that lightly melted the ABS and allowed the bond to form. It was a very tight bonding.

The closest I've found to that, and probably your best bet if you don't mind buying it, is Plastruct Plastic Weld. This may even be the hobby version of the stuff I used back in the day, the effect is the same based on the description. 

I also understand that acetone (otherwise known as nail polish remover) can have a similar effect on plastics of various sorts. If you have some junk plastic to test with, this is worth trying. You're not using a lot, you just need to dip the parts to be bonded in or brush it on with a non-plastic brush or cotton swab.