My computer keeps disconnecting at irregular intervals. It my go for half a day, just an hour or maybe minutes and the diagnostic mode comes on to check the connectivity. I have disconnected the modem, and sometimes the internet light goes off or flashes off and on. Sometimes the activity light is off.

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Originally Posted by tculberson

How can you tell if your modem is broken?

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The easiest way is to replace it with a known good modem and see if the issue persists.

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Originally Posted by tculberson

the diagnostic mode comes on to check the connectivity

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If you are referring to Windows', see You receive a "Limited or no connectivity" message on a computer that is connected to the Internet by a DSL modem or by a cable modem after you install Windows XP Service Pack 2. However, most of the times I've encountered on again-off again network connectivity situations where the connectivity oscillates, it was due to a physically damaged jack or network adapter or electrical damage due to a surge.

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Originally Posted by tculberson

I have disconnected the modem, and sometimes the internet light goes off or flashes off and on. Sometimes the activity light is off.

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Regardless of the modem, I would expect the activity light to be off when there is no activity. Otherwise, without knowing the modem model it is impossible to say whether the Internet light is behaving as it should. Generally, though they are off when the WAN connection is down or flashing when a connection like PPP is being negotiated.