I encountered this issue with both Logmein and VNC so the issue would appear to be with the Mac client not the application used to connect to it with.
A bit of googling found this link which has solution (for me at least). YMMV.
SSH to the client, use ps to find pid of the loginwindow and kill it. I've done so and now both vnc and logmein display correctly. Hope this helps someone stumbling like i did upon this post.
EXCELLENT and thank you for editing color quality to get of the the black/blank screen - it worked! What a hassle, come one LogMeIn - get this fixed. It's been happening for YEARS.