Much of this depends on the type of site you're running.
Is the site CPU heavy? Does it make use of dynamic technologies like PHP? Does it use additional dynamic components (like a MySQL back-end)?
Or is it primarily a static site?
If it's primarily a static site, then 1GB RAM and a P4 should be just fine for you.
If it's a dynamic site then whether or not that system will work for you depends completely on the resource usage of your site. If it's computation heavy then you may need more CPU. If it uses a decent amount of memory then you'll need more RAM. If it's makes heavy use of disk I/O then you will want to consider RAID.
http://www.cpubenchmark.net/cpu_list.php Even in synthetic tests, a model slightly faster than the 3040, the 3050 is more than twice as fast as a Pentium 4 at 3.0GHz. I think you might do better with a VPS if money is an issue, rather than using old hardware.
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