|You shouldn't be connecting to your neighbors wireless so we will ignore the wireless aspect.|
Modems need to be registered with the ISP. Have you talked to your isp concerning the new modem?
I take it you have only a modem and only a patch cable. The cable could be damaged. Get another.
Talk to your isp concerning the modem registration and your intermittent wan failure. Does not appear to be a issue with the pc or the ps3