Networking 2 comps on a switch with winxp

I'm trying to network two computers on a switch. Neither computer can see the other, but I've networked them before, so I know it's possible. Here's my info:

I can ping each computer from the other.
I don't have dns problems.
I have tried multiple approaches to the windows xp networking wizard
Both Subnets Masks, Default Gateways, and IP Addresses are issued from my ISP
No firewall software is on
Both computers are in the same workgroup
Everything is physically setup correct

Computer 1:
Connection-specific DNS Suffix . : attbi.com
IP Address. . . . . . . . . . . . : 24.16.224.13
Subnet Mask . . . . . . . . . . . : 255.255.240.0
Default Gateway . . . . . . . . . : 24.16.224.1

Computer 2:
IP Address. . . . . . . . . . . . : 24.19.182.145
Subnet Mask . . . . . . . . . . . : 255.255.252.0
Default Gateway . . . . . . . . . : 24.18.180.1

hi
if u r able to pinging then use the xp networksetup wizard first
then give gateway n dns address.

Thanks. Got any links or hints on how to 'give gateway n dns address.'?

Thanks in advance.

PS: Can i do this even though it's issued to me via ISP?

If you want a local network, I'd do things differently. Setup one computer (or a router) with an Internet connection and a local network connection. This local network connection would go to a hub/switch where the second computer would be connected. Within the local network, you'd have addresses like 192.168.0.x. Then, the one external interface on the computer with the Internet connection would have an IP address like 24.19.182.145, in addition ot the internal connection.