Well everything looks set up correctly. Since it does recognize the card and it shows up in ifconfig, I doubt it's the module. The settings all look fine, unless there is something im not aware or about your setup(like different routes, additional ethernet cards in your machine, or anything else).
The problem could be physical. Check the cable your using on another machine make sure it's working properly, check the card in another machine if possible to see if it works in there. I don't understand why you would ever need to unplug the ethernet (cable, card, anything...) to ping.

Are you using DHCP or static IP addressing? Try using DHCP and just type in 'dhcpcd' at the root prompt and it will set all that up for you automatically.