Type "/sbin/ifconfig eth0" at the command prompt. If you see some cryptic looking junk, that's good. If you see something like "eth0: device not found" then your card isn't detected. Since your card is fairly standard issue and you say it is detected, I'll assume it actually is, unless you say otherwise after running ifconfig.
The next piece of information is how the card should be configured, i.e. do you have a static IP address or do you use DHCP? If you use DHCP, life is pretty simple, you can usually just type dhcpcd to start the DHCP client and it should get an IP address and set up everything for you. If it fails, then there's some problem with your DHCP server -- I suspect this might be what's giving you those failed messages.
You can probably use a static IP address until you figure out the problem. Do you know what IP addresses are used on your network? If your IP address is supposed to be, for instance, 192.168.0.10 you would do:
ifconfig eth0 192.168.0.10 netmask 255.255.255.0 up
(change the netmask if it's different for your subnet).
If you have a default gateway say at 192.168.0.1 you set that up with:
route add default gw 192.168.0.1
You'll have to add your nameservers to /etc/resolv.conf and you should be set. A reolv.conf lines looks like:
where x.y.z.w is the IP address of the nameserver.