There are two major issues that it could likely be, and there's a few extra bits that are worth knowing. We'll start with the knowledge.
1) Most cable modems require power cycling when switching between devices plugged in, as they tie communications to the MAC address of the ethernet adapter of the device plugged in.
2) Most cable ISPs will not let the cable modem communicate with devices that have MAC addresses associated with routers.
3) All cable modems will have some sort of diagnostics portal page that you can access, and this page can be useful in determining whether there's noise on the lines or not (basically cabling issue, either yours or the cable company's end).
Here's a guide for the ranges you should expect. For Motorola/Arris modems, that portal address is
http://192.168.100.1/ and should be reachable even behind most routers.
The two most common failure points after a fresh install is either the MAC address issue or line noise inside the house on a cheap coupler/splitter/wall jack or from older RJ59 (or lower spec) cabling. RJ59 should work but really old cable could have problems, and newer RJ6 is the preferred used coax cable. Typically, when the cable tech is sent out for a new service hookup, they're checking signal strength to the DMARC point (the box on the house that they hook up to to get to the wiring inside) to ensure service is usable. This is why if it is a signal/noise issue, it's likely on your cabling end. Given you didn't mention error lights blinking, I doubt it's that however, though it doesn't hurt to check the signal diagnostic page anyway.
That said, it's most likely the MAC address issue, and it's really easy to fix. On all routers, somewhere in the settings, there should be a WAN MAC address clone option and some sort of "Get Current PC MAC Address button" or something along those lines. (WAN is Wide Area Network, by the way... it's the end of the router that plugs into the modem.) Use this to change the MAC address of the router to that of your computer. While you're there, make sure your router is set to DHCP on the WAN end and not Static IP, PPPoE, PPTP or L2TP or whatnot. Once those settings are saved, power down the modem and the router and bring up the modem only. Once the lights go stable, power up the router and let those lights go stable as well. Then check your connection. Knock wood, it should all work. If not, let us know.