Time Warner Cable here has been a little flaky. It was not our modem or router.
As to your router, you did try it with no router. Time to swap routers again.
Note: Moderator edited for content.
This week my internet has been acting up. I would get booted and then day or so later back on just to get booted again 24 hours later. When booted I still connect to the cisco linksys router but it reads limited access and no internet. If I connect my msi laptop Windows 8 to the zyxel modem i have internet same for my xbox one. If i plug my other windows 8 dell laptop into the modem here is the kicker that doesnt connect.
I called my provider oxford networks and they said its not them its the router. Fine I go out and buy a new linksys router n300 and same issue nothing changes. I call linksys and troubleshoot with them for a long time for them to say our router is too old and we need a new one. OLD I JUST BOUGHT IT LESS THEN 24 HOURS AGO. I need a $150 router and not the $50 router. He recommends a ac router. I haven't changed modems so what is with all these issues any ideas please help.

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