Surface Pro 3 is not charging; power connector LED is blinking

Your Surface Pro 3 is charging intermittently, i.e. switching from charging to not charging every 10 seconds. Check for the white LED in the power connecter that attached to the right side of your Surface, and see if its blinking.

If yes, then check whether you have other devices attached to your Surface charger (such as your Lumia phone), and disconnect it.

If this solves your issue, the problem is that the charging was not managing to charge both at the same time (especially if you were charging your cellphone using a USB 3.0 cable).