Microcontroller PIC32MX
The VDD/VSS (VCC/GND) pins must be connected for the chip to work. These pins are not internally connected with each other in most cases, and they power different parts of the logic inside the chip (peripherals). 

Take a look at the data sheet, this is for the PIC23MX5XX/6XX/7XX but they are the same for all PIC32MX families:



You must also use decoupling capacitors:



And here is the recommended minimum connections:



Additionally, you need to provide the chip with 3.3V only, so you need to use a voltage regulator to translate the 5V from USB to 3.3V for the power pins. 

Pay special attention to I/O especially if it is powered via a different source. If you inject 3.3V into a 3.3V pin, you will burn out the chip when it is not powered. You can provide up to 3.2V into a 5V tolerant pin without burning it out, but any more than that will cause damage.

VBUS pin is an input that monitors the USB bus power, it does not power the chip. VUSB3v3 is a transciever supply, and should be connected to VDD if USB is not used, however do not provide more than 3.3V into this pin (as the name implies).