Im not saying there is an issue with your Network card, its just ESXi does not have a suitable driver for it. Im assuming you are using Realtek RTL8171E gigabit ethernet (got this from HP site). There was a blog post from Vladan Seget on how to install the 8169 driver vib. http://www.vladan.fr/realtek-8169-nics-not-detected-under-esxi-5-5/
But again this is for 8169. Im not sure if there is a driver available for 8171 (8171and even 8169 is not in VMware supported list)