Exiting all programs "launched after startup" did not change a thing
(veryfied by process listings). Other computers on the network
behaved without this problem.
Fortunately, it so happened that at this moment I could reboot the
system without much data loss - and this fixed the problem. (Hard
reset after shutdown, but no power cycle.)
Anyone knowing what it could be, and whether it is fixable without
reboot?
Thanks,
Ilya