I see the discussion has begun.
My first point is : When I left dialup for DSL back in 1998 (Yes 1998, MPower 8Mbps ADSL), the computer systems that you see out there now didn't exist and my personal best system was a P166-MMX with 64M RAM, and my 486 DX-2 20M running Win95 on the Internet well - it still lives.
DSL will win, and any computer that is capable of receiving and processing more data than it is throttled to can benefit from higher.
Modem, max 57600 bps, do some copmpression and maybe double sustained throughput. DSL and various versions will either install or use an existing 10,000,000bps (10Mbps)ethernet card, or 100 Mbps, (100 million bps).
So is there an Internet for us out there that will provide the data that quickly? Not really. The top speed I have been on was 8Mbps, Comcast now boasts 6Mbps and Earthlink at 3Mbps. Your network card will be much faster than your Internet.
So ... systems MUCH slower than the one you described have utilized whatever DSL could throw at them. And just like any other computing environment, if you over task your multi-tsking capabilities, it will slow your ability to process your internet once the files have arrived ... this is a processing problem and not a dialup or DSL problem - so don't try to over task with lots of other software running.
To help accomplish this, Invest in a router! Which will handle the firewall between your systems (LAN) and the Internet (WAN) leaving your computer free of that software burden.
A proper install is DSL goes to their modem, to your router, to your PCs - you are now behind a firewall.
The job of a properly installed router is to only allow information that was requested from your side (LAN) to pass through from the Internet side (WAN).
(read up on routers)
deium