Internet Cookie Network Problem

[excessum]

OK here is the odd problem I am having with my network. I have been using a Linksys 4 Port Router for quite sometime now without any problems what so ever until NOW. The problem I am getting right now is that, when I have all the computers running I am unable to connect to cookie required protected sites (ie. gmail.com, myspace.com, gotfrag.com, etc..) not only is it MY computer but its like that for EVERYONE on my network. Usually I get an error that tells me the site would not let me connect to the URL because I did not enable cookies, and the router and browser are BOTH accepting cookies at all times. I tried re-configguring the router, rebooting it, re-booting the modem. However, whats odd is that when I take the CAT-5 from the modem and put it on the regular ports with the other computers, I think it was 2ND PORT, and I move a couple computers around on the ports everything magically works, without even having the modem connection in the INTERNET port on the ROUTER. This totally boggles my mind, I have tried every bit of troubleshooting I can. Nevertheless, I am still going to continue trying to figure this problem out but until then I would like to see what you guys might know about this or have experienced this because it is 100% random to me.