Hi Fred - SUCCESS!!!
I'd tried putting my computer's password in that field 'numerous' times, but then thought, perhaps, going on all that's been said/covered in this thread, if I copied the contents of the file 'gui_rpc_auth.cfg' into the password field and see what happens. Thankfully, my BoincTasks session then jumped into life and works
Later on today, I'll try getting BoincTasks on the other computer I'd been having issues with to work using this same technique if the 'proper' way doesn't click.
As to why this didn't work automatically as it's supposed to - who knows (and now, quite frankly, considering we've got a 'workaround', who cares).
Once again, thank you for all your help and patience in resolving this matter.
I'd tried putting my computer's password in that field 'numerous' times, but then thought, perhaps, going on all that's been said/covered in this thread, if I copied the contents of the file 'gui_rpc_auth.cfg' into the password field and see what happens. Thankfully, my BoincTasks session then jumped into life and works

Later on today, I'll try getting BoincTasks on the other computer I'd been having issues with to work using this same technique if the 'proper' way doesn't click.
As to why this didn't work automatically as it's supposed to - who knows (and now, quite frankly, considering we've got a 'workaround', who cares).
Once again, thank you for all your help and patience in resolving this matter.