Hi,
We have sent you e-mail few days ago, I will post it here as well for other users reference.
We have not met a problem with OnMouseOver before. I would recommend you to try to change the path of all images to full URLs, e.g.:
<map name="map_r5_c4Map"><area shape="rect" coords="1,1,20,74" href="http://www.lawsocietysa.asn.au/other/collaborative_law.asp" alt="sa-4"
onMouseOut="MM_swapImage('map_r3_c3','','http://<domain name>/Images/map_r3_c3.aspx','map_r2_c4','',''http://<domain name>/Images/map_r2_c4.aspx','map_r4_c4','',''http://<domain name>/Images/map_r4_c4.aspx','map_r5_c4','',''http://<domain name>/Images/map_r5_c4.aspx',1);"
onMouseOver="MM_swapImage('map_r3_c3','',''http://<domain name>/Images/map_SA-Roll2.aspx','map_r2_c4','',''http://<domain name>/Images/map_SA-Roll1.aspx','map_r4_c4','',''http://<domain name>/Images/map_SA-Roll4..aspx','map_r5_c4','',''http://<domain name>/Images/map_SA-Roll3.aspx',1);" />
</map>
Unless it helps please try to add the code to blank page which does not inherit from anything and test it. It would say if a different web part affects it.
Eventually, you could create a simple test site where would be only the map code and appropriate images and export this simple site. We would need especially the images and see the content structure.
Best Regards,
Juraj Ondrus