Browsing some old VHS videos looking for stuff to dump, I came across Lawnmower Man 2: Beyond Cyberspace and gave it a quick viewing. It's not a good movie by any stretch of the imagination, but then it struck me that it does have some similarities to The Matrix. (I didn't get to watch it all though as it was fairly dire). By the way The Wachowski Brothers are in fact sisters.
EDIT: I stuck a trailer on LM2, so you can judge for yourselves.