Internet Connection is Messed Up

I have a DSL connection. All rooms in my house have parallel phone connections. I connected a modem in one room and connected that modem to a computer using an ethernet cable. I want to connect another computer in a different room to the Internet too, so I connected an identical modem to the second computer and linked it to the phone outlet in that room. Now, the Internet is messed up. Have I done something wrong?
