My Surface 2 would not turn on. I tried every trick from the Internet. No luck. I even tried another charger. No luck.
Then I went on vacation for 30 days. On my return I thought I would charge it overnight. Next morning I pressed the power button and it turned on!!!!!
I figure it must have been in 'sleep' mode (MS has a lot of problems with it). The battery must have drained completely and therefore it was no longer in sleep mode. Once recharged it worked normally.
I have turned off 'sleep' mode and the tablet has been working fine!