You said you can get to your router. That implies you have an IP address and sub-net mask set. You can not ping other hosts on your own lan? I would check two things, make sure your machine and the other hosts are on the same sub-net, and the mask on your machine matches the mask others are using.
To see your setup at a command prompt type - "/sbin/ifconfig" ( without quotes ). Here is what mine looks like.
[cliff@sluggy cliff]$ /sbin/ifconfig
eth0 Link encap:Ethernet HWaddr 00:D0:B7:26:B3:78
inet addr:192.168.1.13 Bcast:192.168.1.255 Mask:255.255.255.0
UP BROADCAST RUNNING MULTICAST MTU:1500 Metric:1
RX packets:4529 errors:0 dropped:0 overruns:0 frame:0
TX packets:6837 errors:0 dropped:0 overruns:0 carrier:0
RX bytes:3442220 (3.2 Mb) TX bytes:506254 (494.3 Kb)
Interrupt:11 Base address:0xb000
lo Link encap:Local Loopback
inet addr:127.0.0.1 Mask:255.0.0.0
UP LOOPBACK RUNNING MTU:16436 Metric:1
RX packets:241 errors:0 dropped:0 overruns:0 frame:0
TX packets:241 errors:0 dropped:0 overruns:0 carrier:0
RX bytes:21434 (20.9 Kb) TX bytes:21434 (20.9 Kb)
If your sub-net mask and IP address are in the same sub-net as others, ping should work.
To get the internet working, you need the correct gateway address configured, and you may need to find out what the DNS addresses are, and configure those. Get ping working first, then work on outside access.