ive had the same issues and it was with both my computer and router. i had from my moden a cable runnin to a linksys router (<3) and then to a cisco switch (again <3) but i ended up switching wireless channels on my router and it was fixed. running cables suck man my dad is an electrician and ive had to help him in our house with electrical pulling, i wired my room with cat6 and it was a bitch. the only thing i could think of is turn off everything connected on your network, i.e your xbox and computer(s) and then power down your router THEN your modem, wait half an hour or have no patience and wait 10 mins, then power in this order, your modem, then router, then xbox, with your computer off test the xbox, and if it plays fine then go ahead and turn on your pc if troubbles return you shall know its your pc, if not your golden.
now if the problems do continue, run spyware and virius and all that fancy shit on your comp, then give er another go. if this doesnt work lemme know and ill do some research for ya ive got a buddy who is a computer repair tech hes usually rght about these things and has helped me in the past.
-sean
<3 linksys and cisco