Been having the annoying red x / slow charging / trouble turning on issue on my Tab 10.1. Thanks for all the suggestions, obviously a known issue!! Tried many leads and Samsung plugs but made no difference.
What worked for me - holding down the power and volume buttons for about a minute. The Samsung Galaxy Tab 10.1 logo flashed up every 10 seconds or so. When I let go it started up normally and there was a white lightening flash on the battery icon as normal.
Thanks guys