OnDemand uses the internet, and the older TiVo boxes have an in-built connection that's separate from your home broadband. Do you get any error codes/messages when OnDemand fails? You should do, and that'll give a good clue as to the reason for your problems.
Also, on the front-left of your TiVo are a series of green lights. Does the heartbeat light (look for the painted symbols on the box) flash when you have VoD problems? That will mean the inbuilt connection is failing, and if so - will explain VoD not working.
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