SawMan,
I put Linux Mint 16 (Petra) onto a Compaq Evo N610c not long ago. The spec. is 1.8GHz single-core, with 1GB RAM. I have a D-Link DWL-G650 wifi adapter that was found and configured by the OS, so I was quite impressed by that.
I've installed Libre Office (or rather it was installed in the setup routine), and I can browse the web and do some rudimentary office-type work.
It's certainly not fast, but it's not impossibly / glacially slow. I have to say that it's noticeably slower at doing the above than the equivalent Windows XP & Office XP installation it ran throughout its working life (2002 - 2008).
But it won't run Win 7, so Linux is an improvement over that!
SD