If you only have the Digital Starter package are any on demand channels not available to you. I realize the premium channels won't be, but are you restricted from any of the others. For example BBC America is not available in the Digital Starter package, could you access it on demand though.
There are selected BBC America shows available to you through OnDemand, even though you have the Digital Starter package. I have the same package, and use this to keep-up with Dr. Who. Note, that these shows are usually put into the OnDemand menu after some delay. With Dr. Who, it's about a week. With others, it may be months after their initial airing.
You can find the BBC-A shows by scrolling to TV Networks > BBC America.