Ajc,
It seems as if Windows is not recognizing its own Jet drivers for some reason.
First thing to try is this: if you can get EA up at all, from the start menu rather than by clicking on an EAP file, use the main menu to open the Tools / Options dialog. Check the "Use Jet 4.0 - requires restart" box, close EA, and restart. See if this resolves your problem.
If the above does not work, you may be able to register the driver you have by running regsvr32 from the command line, but I cannot say for sure if this could have other effects.
Another option may be to install a recent version of MDAC. The most recent versions (since about 2.6 or 2.7, but I don't remember for sure) do not contain the Jet drivers, but they may set them up for you if they are there. You might be able to find an earlier version and install that.
Finally, you could install a recent (perhaps since "97") version of Access, or perhaps even Office or Excel or Project (which may install Jet drivers).
If the above don't work at first, keep watching for replies on this thread, since the Sparx folks and other users have probably seen this at some time.
HTH, David