EDIT: The part order was incorrect. I was using an Atmega32 and not an Atmega32u4.
I've been beating my head against the wall trying to get this to work. I've looked up any and all resources I could find online and it looks like this should be a really simple task, but if there's one thing I know about computers and electronics, there's no such thing as easy.
I ordered a few Atmega32u4 with the intention of loading the Arduino bootloader for the Leonardo onto it so that others in the department where I work can easily work on my project if they need to. I know this is possible because I am using the schematics used by a coworker in the department to accomplish the same thing. However, using an AVRISP mkII I always get this error:
avrdude: stk500v2_command(): command failed
avrdude: stk500v2_program_enable(): bad AVRISPmkII connection status: Target not detected
Error while burning bootloader.
avrdude: initialization failed, rc=-1
Double check connections and try again, or use -F to override
this check.
I also get the default (Yikes!) no connection error when trying to use an Arduino UNO as my ISP. Here is the schematic I am using:  It is also worth noting that **when I connect UGND to GND the chip catches on fire**. What the hell am I doing wrong?