I am a bit late to the party, but am having a similar problem with my Surface Pro One. From time to time I would have to jiggle the plug to get the blue light to come on, but about two weeks go, my "low battery" icon popped up and I plugged the charger in. This time, no matter how I jiggled the connector, no blue light, so I left it on all day, but nothing. I thought the charger had failed, so I ordered another, which arrived today. Same result. I have cleaned the port and connector. At this point, the battery is so spent that the tablet turns itself off as soon as it fires up. Am I looking at needing a replacement battery?