In a forum someone pointed out that this may have to do with the TDR (Timeout Detection and Recovery), part of the WDDM which is part of Windows Vista and later, but NOT XP. Hence, the advice I got was to "switch off" this feature in Windows10 by adding the following registry entry in HKEY_LOCAL_MACHINE\SYSTEM\ControlSet001\Control\GraphicsDrivers: QWord "TdrLevel" with value "0". This, so to say, imitates what I had in WindowsXP, i.e. NO Tdr at all.

However, the problem is that once I add this registry entry and restart the PC and Boinc, Boinc tells me "no usable GPU found" in the event log.
So, it seems that BOINC is making a check regarding presence or absence of TDR - is this correct?
If so, is there a way to eliminate this check?

Not to be listened by boinc's admins is like a Dante's "contrappasso": gpugrid admins don't listen their volunteers. :-P

GPU Grid is down. ...

Going blind I would not know but a quick forum search reveals you can set gpu snoozing using boinccmd tool per https://boinc.berkeley.edu/dev/forum_thread.php?id=6071

Just because somebody is a wizard at protein binding energies, doesn't necessarily mean they're red hot at computer security! That's a problem which affects all small-staff BOINC projects.

Their website security certificate expired

Yes, the only thing that the BOINC installer does (for Windows at least) is to remove the old BOINC program files (boinc.exe, boinmgr.exe, boinccmd.exe etc.) and libraries and then install the new ones.

If you're using a modern client, like the recommended v7.6.22, the easiest way to update configurations is to use the Event Log Options tool (Ctrl+Shift+F) - make a trivial change and click 'OK'. That creates a template cc_config.xml file with every possible tag present, and all spelled correctly :-) Then just modify 0 to 1, or whatever, for the tag you need. Did I say I restarted the primary client after making that change? It feels like one which would only take effect at startup, rather than through 'read config files' like some others.

You are very close, but your cc_config.xml is not formatted correctly. See http://boinc.berkeley.edu/wiki/Client_configuration
You are missing some tags.

OK, as I suspected, curiosity got the better of me. I created the two batch files BobCat13 suggested in the message I'm replying to.

And it failed. Watching the changes in the second data directory, I saw a file stderrdae.txt being created, with the contents

05-May-2016 15:50:59 Another instance of BOINC is running.
GLE: Cannot create a file when that file already exists.

 (0xb7)

Armed with that information, I edited the cc_config.xml file for the first (originally running) instance, with the

<allow_multiple_clients>1</allow_multiple_clients>

option, and restarted the first client. After that, everything worked as advertised. Two different clients running (two instances of boinc.exe in Task Manager), two different instances of boincmgr.exe in Task Manager as well, two different displays on screen with different project lists, etc. etc.

@Erich, what firewall do you use, and did you add boinc.exe and boincmgr.exe to it? If just the Windows firewall, what are the settings used?