Normally when they start up they go through a sequence that looks for a signal at that turns on the first light after power called downstream that scans for signals. The light should come on even if there is no signal, so it seems like your modem is not working. If it has a battery, did you remove the battery also?
Since there is a signal at the TV, did you try connecting it to the cable instead of the tv convertor box to see if it works there?
If it doesn't do anything maybe it is dead.
It is possible they are doing maintenance on the Internet service. The Internet uses a different set of frequencies from the cable service.
I had no Internet the other night in MN but still had cable. They were updating the Internet. Ended up with 8 bonded downstream channels and 2 bonded upstream channels when it was back up the next morning.
The light should come on even if there is no signal.
Yes. it should first "come on" in a blinking fashion to indicate that the modem is ranging / searching for a downstream channel/s to lock on to. If it find one / them, it should then go solidly lit.