Yup in the big one in the middle that gets hot.
Looking at the schematic here: http://www.sparkfun.com/datasheets/DevTools/Arduino/Ardumoto_v13.pdf
Apart from the protection diodes, the motor connections pretty much go straight out from the chip. I think your chip is blown.
But also just check you haven't got any snippings of wire or blobs of solder shorting the pins on the chip. Give the whole board a close inspection.
Save the shield for a project where you only need one motor or just want to go forwards