Sounds more like a TV issue than the TiVo. Sorry lot's of potentially dumb questions but have to ask...
Have you plugged the TiVo output into the TV? What connector have you used? (HDMI?) Is the correct input selected on the TV?
You could try another HDMI input on your TV if it has one, or change to the component cables included with the TiVo and see what happens (Make sure you change the input setting on the TV to match the cables)
If the component works then potentially a faulty HDMI cable included.
Always be yourself, unless you can be Batman, then always be the Batman
I plugged in one I had bought off TM this week also and it took ages for the picture to appear. I was getting worried so I plugged in a composite [yellow] video plug but then while I was doing that suddently the image came up saying it was powering up. Once mine had recognised the HDMI connection it switched to 1080I fixed, also while it is booting you can try a different HDMI socket, mine didn't show a picture until I changed socket. Maybe something to do with the aforementioned HDMI handshaking.
Have you got a working broadband connection plugged in? You need it for first boot. With the poor tech support, your best move is to take it to a friend who owns one and plug it in in place of theirs. That'll at least verify that it works and enable you to take it home and start it up. (It'll have its startup information installed)