"Sometimes the adapter connecting the battery to the motherboard gets loose from unsafe carrying. I've opened this laptop a few times, changing the hdd, ram, and this has happened to me a few times. To illustrate this better I attached a link to the part I am referring to. (my laptop disassembled ) Once you disassemble the laptop, it should be a quick fix.
You may need to replace your ASUS Q501LA battery. I met the same problem as you, and I bought a new ASUS Q501LA battery at this site: http://www.laptop-batteries.com.au/compu.... It makes my laptop come to life. satisfied with the battery.