Hi, I had this problem just this morning with my Acer Aspire E1-572G: battery and power lights both on, memory light flickering. I tried all the online solutions - battery in, battery out, power button holding, plug, unplug, hold battery and dance in a circle singing ABBA - to no avail.
I then decided to leave it sitting for awhile in the 'on' state, let it sit on the naughty step and think about what it'd done, and after about 20 minutes ignoring it (brushed my teeth, did the washing up, read a book) it booted up all on it's own. No idea why. I'm not a techie. Maybe an update or something?
Anyway, for others to try, turning it on then walking away for half an hour may do the trick.
I'm about to run a virus check too, just in cases.