You probably don't need a new computer; there's stuff running that's slowing it down.
Probably stuff you don't really need running.
After your computer boots, the only things that you need to be running (starting automatically) are hardware drivers--motherboard, video and sound as well as any other HARDWARE you have, and security programs: firewall, antivirus and antispyware.
If your computer only goes slow when connected online, then you might install a firewall that does outbound monitoring (like ZoneAlarm) so you can see if anything is repeatedly using the network without you telling it to. (There is a common problem with the settings of Windows Messenger defaulting to "scan network for friends when idle", and this slows down a lof of people's PC's) Security programs will update once when you reboot, but they should stay silent the rest of the time.
About the only reason one -needs- a fast computer is to play current 3-D action games.
~