56K this prob wont do anything but it is worth a try.
i presume you are on XP.
Click start then in the run type cmd
then you will get a dos screen, then type ipconfig and hit return
then write down the IP address subnestmask and default gateway
it should be somthing like 192.168.1.10 / 255.255.255.0 / 192.168.1.1
once you have made a note of that type exit
Then goto control pannel and network connections, right click on your LAN connection then go to properties. right at the bottom there should be a TCP IP go to that one and and change the setting from obtain a IP address auto to static IP fill in the fields with the ones you jotted and click apply.
As said this may not help.
The other thing is you may want to look at your router settings, i have got mine setup so when i go on the net it contacts my ISP and get a connection on demand otherwise it disconects.
Hope this helps