I burned an Arduino bootloader onto the Atmega32u4 (installed on my own PCB) using the Arduino app and the Atmel AVR ISP mkII, and am now trying to program it. The burn was completed successfully ("burn done") according to the app, but when plugging the board via USB, it doesn't show up on the list of available serial ports. The connections seem to be fine from a basic inspection (the USB correctly powers the rest of the board) so I'm not sure why it isn't getting recognized by the computer.
I noticed that the UCAP pin is connected to both VCC and the 1uF cap in my schematic (as well as in the lilypad's), but in the atmega's datasheet, they don't connect UCAP to VCC. Is that maybe the reason?
My guess is that is not the reason. Perhaps you need to load a driver on your computer. Are you able to connect to a manufactured Lilypad USB? Perhaps connect your board to another computer and see if it works. Check that ground is connected in all the right places.