Well the internet connection doesn't appear to be any problem so it
may well be the generic drivers that the ATI card is running under,
though as gord_lib says the bottleneck could be the CPU or even the
RAM speed. Adding a graphics card that has Ubuntu driver support may
be all you need and as your demands aren't that high then a mid-range
NVidia is the way to go. One thought, with such a slow PC it's maybe
an AGP card and there's nothing like the range available for this old
graphics format now, so you may have to go with what you can find.