Offline Modem. Tried reboot.?
So you see your router, the problem lies between the modem and your ISP. Any good ISP should be able to put the modem into loopback mode, so packets go from them, inbound to your modem and back. Ask your ISP if they can do a loopback test. I doubt it will work if the modem isn't online, however. You didn't mention what type of connection you have (DSL/Cable/Fiber) and if your modem is integrated router or standalone.
Turn off everything, the modem, the router, and things that attach to it. Then boot modem. When the lights settle don, boot router. When lights settle down, boot first computer. Retry test. If still fail, shut down modem. Connect computer directly to modem. Boot modem. Boot computer. Retry test. If still fail, replace wires. do the boot sequence again. Retry test. THEN call the ISP. Since the router is usually yours, they have no interest in supporting it.
Turtle Bay 777
Try unplugging the modem from both the power and the telephone line. Are you using the provided filter between the 'phone socket and the modem? Use it. Reconnect the phone line first then reconnect the power.