Slow screen refresh

I have a Windows XP SP2 built PC, connected to Broadband 2Mb via a BT Voyager modem.
I also have a 2nd PC, 'ME' Built Celeron 566 with 256Mb RAM & 16Mb Voodoo PCI Graphics Card.
This PC is connected via twisted Ethernet cable for Internet sharing, via a 10/100 Ethernet card.

When using the 'ME' built PC for internet access, logging-in and screen refresh is very very slow. Sometimes the connection is actually lost & I have to close Internet Explorer down & re-open.
I appreciate surfing is going to be slower than the main XP machine, but I would expect the 'ME' built PC to be faster than it actually is.

Could the Graphics Card be to blame, or can there be some Firewall or other setting / conflict.

To add to this, it appears that the two PC's appear to fight for Internet access. Also, if the two PC's are connected to the Internet, I am unable to reach my Outlook mailboxes on the ISP server on the XP machine.

Perhaps I should try & delete & re-install my Network Connections. How do I remove everything in the Network Connections window, so that I can re-install?