nothing for ethernet shows in the picture
but according to http://www.dell.com/support/home/us/en/04/product-support/product/precision-t1600/drivers there are 2 ethernet cards that it can be.
one being intel the other broadcom.
for intel try http://www.insanelymac.com/forum/topic/304235-intelmausiethernetkext-for-intel-onboard-lan/
and if broadcom try http://www.insanelymac.com/forum/topic/304337-bcm57xx-network-with-native-apple-drivers-oob-no-patching/
i guess you can look in windows or linux to see what you have.