Well,
you missed to tell what OS are running on those PCs. Also what are settings for each of the cards and for your DSL modem.
To avoid problems, use router, which will ensure that both PCs have internet all the time, and it will protect your network by closing ports.
They are cheap (30-40 US$) and once set, they work for a looong time.
Check
this link.
Other proper way to set up a network like on picture above is to use
IPCop on the PC1. This require more work, and it is a bit harder to mentain, but results are the same as with the router. It is a bit more sequre, but additional sequirity come with the price. You have to set it up, and mentain it.