hmmm.....time and tiny were bad but compaq were the worst i have found for 'special' software.
couple of things to check first here, are you using an original restore disk from time or did you get your own XP disk?
have you tried removing the modem?
as i see it, if there are no bios settings it could be that each time you boot, the pc 'sees' the modem and keeps the drivers/software in there, using the original restore disk will install the software no matter what you have changed as it will assume everything is still 'as was'.
the software also appears to be running on start up.
if not already done, go to search, type 'msconfig', let it run and there will be some files show up, the one you need is grey with a red line at the top, sticking up at a slight angle...click on it to open msconfig, go to the end tab 'startup' and click on it.
from here you can stop any progs from auto starting....(actually, your best bet is to stop all except firewall/anti-virus as this will speed boot time up)
you may have to physically go into the registry should all else fail and manually delete the entries....if you have never dabbled in the registry then please take extreme care or find someone that knows the way round.
once in the reg, search for supanet and delete all entries you find.....the problem here could be that the software might not actually use 'supanet' in its name.(hence the need for great care).
also, remove the modem from system properties then reboot.
ian
July 2008