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.
after we swap out a router we are no longer able to gain connection through logmein unattended. 1 of the pc show black screen the other would not even connect. The one that show black screen also is not stable on its connection either. its a hit or miss. However, rescue works fine for both. This happened with other setup before but somehow resolved itself. trying to figure out what would be the cause of this.