If you are not getting 12V at the lead ends and the cables are good then the only thing left is the transformer. You could take a look at the wiring leading to the transformer but other than that...
Could be rectifier, diodes, transformer, the list goes on.
YAH166B Snap-On Battery Charger Parts List
Toss it. It's junk. I've had three or four of those units go bad and the Snap-On dealer just laughed when I asked about warranty.
Not knocking Snap-On, I'm definitely a Snap-On kind of guy but their electronics stuff just doesn't hold up.