Due to a inductive surge created when a coil is toggled, a standard 1N4001 diode is usually placed across each transistor as shown in the figure, providing a safe way of dispersing the reverse current without damaging the transistor. Sometimes called a snubbing diode. The TIP120 transistors do not need an external snubbing diode becasue they have a built in diode. So the diodes shown in the drawing are the internal diodes in the TIP120 transistors.
Maybe I'm misreading it, but I thought that meant the exact opposite: that on transistors *without* the internal diode, you'd risk blowing the transistors, but that the TIP120s include it internally and so should be safe. The second paragraph on the linked page has a sentence in boldface specifically stating that you don't need to include the snubber diodes.
So I don't know yet what's wrong here, but I'd look somewhere else first.
those diodes are there to clamp the collector to diode voltage drop. i WOULD PREFER THE DIODES TO BE PUT ACROSS THE COIL as opposed to across the transistor. the question that remains are the diodes fast enough to do the job. if not then the C to B breakdown ocured blowing the whole thing. OR maybe the diodes cannot absorbe the energy from the coil then blewy.
I'd check the PCB for errors. I use AVR, mostly Attiny13L, which at 88 cents each, and still learning... I tend to abuse the hell out of them, and haven't damaged one yet.