It's not exactly clearly the router as it could still be the TV. I myself do not trust the router/modem combination. If you have a good router lying around, I would try putting the modem into Bridge mode and use the separate router and see if your is...
I have just received this particular modem and I have put this in bridge mode. Upon inspection of the casing, it is perforated on all side. While the vents on the top are larger than the sides, it would not harm the modem if it was lying on its side ...
I believe the only reason to stand upright is because of the internal wifi antennas. If you are just using it as a modem, there probably is no reason to stand it upright unless it has air venting from the top of the modem.
