Huge "thank you" to blademaster123 and Toms for keeping a 2013 solution available. Used blademater's "trickle-charge" and saved 2 Asus Transformer computers yesterday!
I used an LG flip phone charger. Couldn't stand the suspense after three hours, so pushed Power and nothing. Then, pushed the top of the Volume button along Asus left side (assuming that was volume up) and then Power; and whamo, my dead computer came back to life. After charging to 20 percent, I plugged in my Asus charger and everything's working again.
Did the same trickle-charge to my son's Asus with same results, Except, his computer seems to have dead battery. Won't charge beyond 12 and then goes down quickly. Plugging the cell-charger in keeps it on but the charge dwindles.
The following worked in 3 hours when NOTHING ELSE I tried did. Thanks, again, blademaster123!
The solution:
"Possibly your battery has been allowed to become flattened to the point where it cannot accept a charge from the wall charger. the best thing to do is to try and trickle charge your tablet from a low voltage/amperage connection. Either a powered on PC USB port to the charging connector on your tablet, or from a low power phone charger (5v/500ma). It has been pretty well documented that lithium batteries do not like to be drained fully & it may be that the battery in your tablet has drained so low that it cannot accept a charge from the Asus a/c charger."