partypooper, even if you do upgrade to a faster system it won't mean your internet connection will run faster. It all depends on what plan you are on through your ISP (Internet Service Provider)

Are you on ADSL, Cable, or Dial Up? if you are close enough to your local exchange you may be able to upgrade your plan and get a faster connection.

You can speed your Computer up with 2 parts, Larger CPU (Chip that runs everything) & more Ram (Memory)