Good thoughts there.
I did some looking up of stuff in the machine in response to those. I didn't find anything untoward.
I'm pretty sure it's not an infection - the check routines run often, and haven't reported as much as a sniff in a very long time.
The PC has a fixed address from the router (192.168.8.110) - that's so that I can access it remotely down the VPN. It's been that for a lot longer than the "request for frog" has been popping up. The router's IP address, set in the PC as default gateway and DNS server, is 192.168.8.1
Firefox and Thunderbird know that the Internet is a direct connection. I don't use IE or OE. The only software that doesn't say that is BOINC, which is set to "Internet Connection (Fall Back)". The other options are stuff like the Frog, "Bluetooth Connection" and "PCI Modem Dial-Up" - the same list as appears in the "Start - Connect To" list.
The "request for frog" seems to pop up at almost random times. Sometimes I'll leave the machine doing nothing, and come back after ten minutes and it's there. Other times, it won't do it for hours.
I wondered if it might be Firefox getting impatient when I've got several tabs open, and the stuff it's trying to get isn't coming fast enough for it. It popped up the window once this evening as I was refreshing several pages, but that may have been a coincidence: it doesn't really tally with the thing popping up the request when I'm not even using the machine.
I wondered about deleting all the connection options (including the Frog) so that the machine wouldn't have the option - but once in a while the ADSL goes down, and then I play round with dial-up to check the ISP status.
Hmmm...