Get verizon fios.
Then you will get speed like this.
I can download a movie in about 10mins.
MP3s take about 2secs to download
Good suggestion, but not everyone has the service/resources to get a plan like that.
Your internet speed depend on multiple things:
how many people are on that same connection
what type of connection (wired/wireless
how fast that connection is in the first place.
etc
The computer itself wouldn't have much to do with it downloading fast (other then maybe using a phone port connection compared to a ethernet/USB connection, but we would need more information on what I said above before we could help you more.
But, if you are only asking to speed your PC up itself. Then RAM, HDD space, and the CPU would be good places to look at first.