Need a default gateway which = your router IP address for internet to work. Also DNS resolving. This is normally automatically set up by DHCP but doesn't appear to be working for you.
There are a number of ways to find this out - command line first
try route at a command prompt it should look something like this
Destination Gateway Genmask Flags Metric Ref Use Iface
192.168.1.0 * 255.255.255.0 U 0 0 0 eth0
default 192.168.1.1 0.0.0.0 UG 0 0 0 eth0
If there is no default gateway then:
route add default gw 192.168.x.x(your router IP address)
should do it (but have a look at the man pages)
If you can then use browser with http://IPnumber
but not with names you then need to get DNS resolving to work. If you know the DNS server IP addresses for your ISP then you can add them to your /etc/resolv.conf (need to su to root to amend this file) as:
All of this can be done using YaST .. network devices .. network card. Click on change button on bottom box then edit and the hostname and nameserver button gets you to the DNS server boxes and the routing button gets you to the default gateway box.
What could have happened is that your machine has got confused by you installing at work and then moving to home. You could always as a first instance use YaST to remove the card, reboot and then it will rediscover it on boot (just like windows) and set it up again.