You mention that you are using a Belkin router?
Some routers (notably Linksys models, although it is not exclusive to them) cannot deal with large amounts of (half)open connections and will drop out.
My router did the same until I adjusted the settings to compensate.
Try running a PC with p2p software without the router and
with a software firewall., a
*personal* suggestion for a free firewall would be
Comodo Firewall
Comodo deal with internet shopping security, it is in their interest to secure your online experience so you can purchase online, thus the companies are more willing to purchase security licenses from Comodo.
Yeah, eliminate the router from the equation and go from there.