Have you tried the preview mode with the Password option selected? There is left to the preview button also a settings button. I've set it to a time longer than the password setting to blank the screen.

Walked over to another machine with 5.10.20 still and it works there too, BUT, there popped up a little Sunbelt Firewall alert window.... and now I can replicate the behaviour. FW off, works, FW on and it does not, now and then. Switch password option off with FW on and it works. Gave BOINC.scr permission to use localhost and port 31416 and it works with PW on and off.

Just never tried the BOINC screensaver before on that one. Sometimes it will, sometimes it does not work, so maybe there is a contention? The Windows in-build firewall though off was also worked over to permit BOINC.scr. It's crud and even interferes when off.

Since you can use any screensaver, compliance to company policy being requirement, take an alternate so your machine is save.

Makes no sence to waste more time on this ghost in the machine.

To get the screensaver to work reliably with the password protect option you need to install as a service then follow this workaround.

Other things that may be causing problems: boinc.exe needs internet and local access through your firewall. boinc.scr, boincmgr.exe, and boinccmd.exe need local access through your firewall.
If you use idle detection in BOINC the screensaver must start after the core client. For example if the preference is set at 3 minutes then the screensaver should come on at 4 minutes.
Go to blank and power settings should be set to the same value, which should be larger than time to start the screensaver.

edit: I forgot to mention that graphics are not supported with VIsta under any circumstances, that should be fixed in the 6.x.x version.