GNU/Linux is really the only way to go.
But I'd certainly try Xubuntu over Ubuntu. (Xubuntu is almost the same thing, just uses a lighter window system that works better for older systems.)
Get the alternate installer too.
If that doesn't work, give puppy linux a go:
http://www.puppylinux.org/
If that doesn't work (and it really should!), then give DSL (above) a go. But this is really, really cut down.
You couldn't really use DSL as a regular operating system. Puppy linux, probably. But Xubuntu is definitely the most comfortable, especially for someone not that used to GNU/Linux systems.