Oh, you wanna run software on this system?
You're screwed.
pull the modem cable out :)
Making the assumption that this custom OS will be binary compatible with other commonplace OSs (just for the sake of allowing the user to have some software), there will still be attacks on either the installed software or simply on the user's gullibility, or maybe other attacks like DNS cache poisoning, where it doesn't matter what computer the user is running.