ATmega32U4: no output
In your second image, the scale is just 10mV. Hence, I would not read too much into that pattern. It's possible that you are just picking up noise. Power supply decoupling caps should not cause you much concern, as long as they are in parallel, and are not blown. Could you provide more detail on how much power the part is drawing when you connect it to the USB port? Does the part overheat?