I had the (sometimes black/ gray/ no screen) issue for Basilisk on my 32 Vista machine.
I tried the above mentioned fixes to no avail. Did some digging around on the web and came across a you tube video that claimed to have a fix. I tried what it suggested, again to no avail. Then I did a variation of it, and it worked like a charm.
Read all the way through prior to trying.
1) Here is the YouTube link
http://www.youtube.com/watch?v=J22uznhj4xs
2) Here is file one which is described.
http://t.bothorel.free.fr/Divers/BasiliskII_win32_20012001.zip
3) Here is file two which is described.
http://gwenole.beauchesne.info/projects/basilisk2/files/BasiliskII-1.0-0.20060501.1.win32.zip
4) I replaced my current Basiliskii.exe for the one listed as new in file two.
5) Next I right clicked on my new Basiliskii.exe icon and went to "properties" and checked "run as administrator".
6) Then I right clicked on the basiliskii gui and went to "properties" and checked "run as administrator".
7) NOTE* I did not check "run in XP compatability mode" for either of the above as the you tube video suggested. (for some reason that didn't work for me and i just happened to try it without checking this option)

Worked like a charm after.
**Now a quick question for you** I have sheepshaver with 0s 9.04 update running great. What os do you recommend should i use for basiliskii so that between the two i will have the most compatibility of all programs? What ROM do you recommend that I use for sheepshaver with 0.04, what about for basilisk with the os you suggest.
Thanks in advance.