It's highly likely something changed with the recent work, so that's the first and best place to look.
By the way - I can't really tell what changed between the time it was starting to when it didn't?
Most immediate problem is the HT end. Those are normally soldered on, so that's easy. Dig the clip out of the coil socket, whittle back a little of the insulation and solder it back onto the lead. Make sure the socket is bright and shiny copper for the best connection.
If you have a multimeter, take an ohm reading from one lead to the other straight through the spark plug caps - should be somewhere around fifteen to twenty thousand ohms.
Do the spark plugs spark when cranking the engine?
I doubt the carburetors suddenly stopped working - unless they're not getting any fuel. So rather than getting upset, tearing your hair out, and pulling the bike apart looking for something obviously broken, it's best to routinely walk through troubleshooting steps to locate the problem. Gotta be smart about this - the shotgun approach is kind of crude and may work sometimes, but not enough to give any real satisfaction. And besides, it can be really expensive buying un-needed new parts.
I don't follow you on the black washer around the prongs. But there is a test for the bean can, but it does require constructing a simple circuit with a light bulb and resistor. Or it can be tested when installed. One of the easiest methods is to disconnect the plug to the bean can and then with the ignition on, ground the center terminal. If the spark plugs spark, when they didn't before, the bean can is bad.