one computer has access to internet, the other doesn't

[John Smith]

I have two computers connected to a router which in turn is connected to
a DSL modem. They can see each other in My Network Places. File transfer
is OK. The one that is running XP sp2 has access to the Internet. The
other can't. It can't ping the DSL modem. The only things it can ping
are other computers on the same network. I shutdown zonealarm, still
can't ping the DSL modem. I switch the cables, no change. That proves
the cables are not the culprit.

Where should I start to tackle the problem?

 

[smlunatick]

I have two computers connected to a router which in turn is connected to
a DSL modem. They can see each other in My Network Places. File transfer
is OK. The one that is running XP sp2 has access to the Internet. The
other can't. It can't ping the DSL modem. The only things it can ping
are other computers on the same network. I shutdown zonealarm, still
can't ping the DSL modem. I switch the cables, no change. That proves
the cables are not the culprit.

Where should I start to tackle the problem?

What IP addresses are the two computers using? How do these IP
adresses get addresses get assigned?