Ok, in that case I have a somewhat simple idea. When you go switching the cable from your computer to the PS3, turn off the modem first. Maybe the problem you are having is the modem did not "let go" of the ZIP address given to your computer when connected to it. Once switched over, power it up again.
I would also suggest conacting your ISP and ask them about the DNS servers' addresses and enter hose into the PS3's connection setting.