Thanks to those who commented.
I tried /etc/init.d/networking stop . When this is done, programs
launch without delay. Of course, this makes it impossible for any
program to access the Internet so it's not a solution!
However, taking gedit as an example,
Normal operation - Internet accessible - gedit launches in 2 seconds.
External problem - Internet inaccessible - gedit takes 60 seconds to launch.
Internal shutdown of networking - gedit launches in 2 seconds.
Maybe this means something, but I am not sure what.
I also found NetworkManager and NetworkManagerDispatcher daemons running.
I tried /etc/init.d/network-manager stop which eliminated one - I
killed the other. This had no effect on the symptoms - gedit and other
still take 60 seconds ot launch.
I also found 8 instances of nfsd and one instance of nfsd4 running.
Tried to kill -9 all of them. This had no effect.