Internet says,"local area cable unplugged" then "now connected" within seconds...?

If all the cabled and wireless are doing the same thing... then your router is powering down and up. Try unplugging the router for about 30 seconds, and then plugging it back in. Examine the DC power adapter itself and the cord for it. See if the power port on the router is loose. Check the wall power outlet itself.

But in the end, you might be looking at spending another $40 to $60 for another router.