Tech support that isn't supportive

All day, we have been having internet issues. It goes down, it is out for awhile, it comes back up. It has been down at least 4 times today, once it was down for over an hour. My system is set up on a high speed cable modem, which runs to a Dlink router, and then to the home network. On the network is a television, two Roku boxes, two desktop PCs, an iPad, two iPhones, and a MacBook. (We are a relatively tech savvy house.) The last time the internet connection was down, we tried: 1. looking at the local network. I could see and access all of the devices on the network from my PC. Local network is working fine. 2. We then tried rebooting the modem. Didn't help, connection still down. 3. Then we tried sending a ping to google.com. It timed out. 4. We then tried sending a ping to the DNS server. It also timed out. I called tech support for my internet provider. By this time, the internet connection is back up, but for how long? The person I got tells me that she needs to reboot the modem. I told her we already tried that, but she insisted. No dice. Then she says that the modem is answering fine, and she thinks my router is the problem. She insists that I need to remove the router and connect the PC directly to the modem. I explain to her that I know that she is working off a script, but I tell her that I am sure that the router is not the problem. She insists, and wants me to disconnect it, and tells me that I need to pay extra for "home networking service" if I want to set up a home network. I hung up. I am not happy with the tech support that I got. Not happy at all.