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ROuter COnfigz
No, "flapping" is not the term for it. Flapping is when the metric on a route jumps up and down. His Linksys router appears to be a simple switch, at least from the view of his PC.
Check to make sure that you're using a straight-through Ethernet cable, and not a crossover or rollover cable.
BTW, chislam, his having the router connected to a modem has nothing at all to do with this.