Thanks for the quick reply!
It has a maximum current rating of only 50ma.
I checked the atmega328 datasheet, and it says that there's a 1..100Kohm resistor connected to the input to the ADC, which should limit the input current to 3.3mA (1..100Kohm?). Also, the ADC is designed for connections with a 10Kohm or less output resistance; since the 3.3V pin outputs a maximum of 50mA then it should fall well within this 10Kohm max. Am I missing something here?
Also, I've completely disconnected everything from the board before connecting it to the PC and I get the same issue. I'll try removing the atmega328 chip and connecting that to my computer at the next opportunity I get.
Thanks for the help.