My Acer Iconia A1-810 won't turn on. It shows the Acer logo, but that's about it.

I am having a similar problem with my Iconia A1-810.  I was at 1% battery, and plugged in the charger.  I kept using it, thinking it would be OK since I was plugged in.  But after about a minute, it shut off, which was OK at the time since I needed to sleep anyway.  I left it charging overnight and into the moning.  Around noon, I unplugged it from the charger and tried to turn it on.  It acted like it usually does, vibrating once and showing the acer logo.  Then the screen went black, and a few seconds later the logo popped on again.  That lasted about a minute, then the screen went black again.  Now when I try to turn it on, it does a quick vibrate and a split-second dim flash on the screen, and nothing.  I have tried the volume/power button combo (both directions on the volume, since it depends on which way it's turned as to which way is the volume increase), as well as the power button and plugging it into the charger combo.  It does the same thing - vibrate once and flash, which will happen repeatedly if I hold down the power button.  I have put it back on the charger, hoping that maybe it just didn't actually charge (the charger that came with it is very loose, and can easily come out either from the unit or the base plug with just a bit of jostling).  But I fear it is needing repair or battery replacement.  I have had it less than a year!

Turned out to be the charger after all.  I switched it to a different spot on mypower strip, triple-checked the connection spots, and left it overnight again.  In the morning, I tried again to turn it on and it powered up as usual.  I seem to have a bad charger set, but a new one is out of my budget.  If I could find my warranty card, I might still be within a year of purchase, but I moved and that piece of paper is lost in the mess...

Thank you for your help!