Mysterious programs with names consisting of 6-8 hexadecimal digits (like
12de734a3.exe) keep trying to access my network on the hour most hours, a
new program every time. Anyone any idea what is going on?

The m/c is running Win Me and has broadband access to the Net via a Netgear
WG111 Wireless USB2 dongle, connecting to a DG834G wireless modem router.
The firewall is the latest free version of Zone Alarm configured with the
computers in the Trusted Zone and the net in the Internet Zone (Duh). these
programs are in Windows/temp and are almost all 63K in size. They try to
access the router in the Trusted Zone, but a lot of programs seem to do that
before accessing the Internet. I keep denying them access as I haven't a
clue what they are. I have had problems recently with a couple of attacks by
the WWWCoolSearch adware parasite but think I have manage to root it out. My
Norton AV is up to date and it says the machine is clean, likewise Spybot
(The NAV is an older version that might not catch some non-virus kinds of
malware, I suppose)

Any help much appreciated as I'm a newbie to networking, and not even sure
where the problem is located here.