Well, I'm still none the wiser, but I have found these four errors:-
The asapiW2k service failed to start due to the following error:
The system cannot find the file specified.
The Fujitsu USB ADSL Loader service failed to start due to the following error:
The service cannot be started, either because it is disabled or because it has no enabled devices associated with it.
AMLI: ACPI BIOS is attempting to read from an illegal IO port address (0xcfc), which lies in the 0xcf8 - 0xcff protected address range. This could lead to system instability. Please contact your system vendor for technical assistance.
AMLI: ACPI BIOS is attempting to write to an illegal IO port address (0xcf8), which lies in the 0xcf8 - 0xcff protected address range. This could lead to system instability. Please contact your system vendor for technical assistance.
The top two don't occur every time, which would fit in with the frequency of the error message, so I would guess it's one of them. The 'Fujitsu USB ADSL Loader service' error must fix itself, because the modem always starts, probably by rebooting itself, so by a process of elimiation, I am working on the theory that it the asapiW2k thing which is the culprit. All I need to do now, is find out what it is. It seems strange that it appears to be related to W2K, which has never been on this machine.
The two AMLI: ACPI BIOS errors have been there for ages, and always appear on the event log at bootup.