several other questions need answering before "we" can give you a complete response.
is this XP or Vista, What CPU? old or new PC. How much free space?
1st. XP performs a whole lot better with 1Gb of RAM, Vista requires a minimum of 1Gb. From your specs i suspect you have XP with 512Mb of RAM with 128Mb shared with the onboard Video, if you can double it to 1Gb. (check the motherboard specs to see what sort of Memory to buy and how much you can install)
2nd. Norton on your low side specs is slowing your PC down everytime you access a file or webpage.
3rd. Broadband make no difference to how fast your PC runs, it is an access point to the internet and the bandwidth of the connection determines how fast the pages load.
If the PC pauses every so often try this to try and clean it up a bit.
go here and download this - http://www.tuneup-software.co.uk/download/ it is a 30 day trial version but fully functional.
Use it to sort what boots with Vista or XP, all those extra software progs that you don't need at start up you can disable them.
It will allow you to clean the registry of all broken links, this in itself can speed up your computer.
It will clean the Temp files, internet files all from this one program. You can also defrag your hard drive, check the free space, run checkdisk, even defrag the registry and edit it, change Windows Icons and much more (I think I will buy shares in this company I recommend it that often)