I am not sure what you would call "normal software", but i have an old machine that is a PIII with a 550Mhz processor and 128MB of RAM(i use it as a file server). I run on it a version of xubuntu(forgot which version, but it is about a year or so old). XFCE runs beautifully on it. Along with all of its software. And with an even lower end machine, you can use even lighter desktop systems.

Of course, you'd need to substitute a few of your regular applications, for example firefox still has a few problems with memory, and so you might want to look at an alternative.