Modem stops working after adding network card

Within one week I encountered two computers showing the same problem, which I haven't been able to solve. This concerns me, since one of these machines is mine. What happened is the following:

Both machines run Windows XP, and use a modem --- in one case an ADSL modem --- to connect to internet. Everything works just fine, until I added a network card to these machines. After that, the modem seems to connect just fine, but DNS is not working. The computer has received the IP addresses of the DNS servers, and I can ping to these addresses. Furthermore, when I try a tracert, I receive the error No hay recursos --- no resources. I have checked all possible corners of Windows XP to find a place where I can disable or criple DNS, but haven't found a solution yet. Does anybody know how to solve this?