Sometimes, after they hook up you cable internet, you can hook a PC to it, but it won't work with a router. The Verizon installers obligation is to make sure a PC can get on the internet. They don't care what happens after they leave. I found this is common with most companies.
What I've had to do in the past when I've connected a router to the cable modem installed by the installer is to leave the router on and power cycle the cable modem. You may have to use a paper clip or some other method to actually power the modem off because many come with battery power in case of a power outage.
In every case for me, this has worked when adding a router to a new cable modem. This could be one solution and is the most common I've found with a new connection. You could have other things going on as well, but this is the quickest and easiest to try.
if a power cycle does not fix the issue. check that your using the right wep key if you put one in your router.
the verizion modems i seen installed now are modems and routers in one. if your has the wifi built in you dont need your router because you have to set your router up as a switch. if the version modem is just a modem with no wifi you have to set your router up to use the mac addresses of your pc. comcast and verizion only allow one mac per household.they know people are going to use more then one pc but the modems look for the mac of the pc it connected too.