Flashing green light means that your Kobo Vox is on. If you can't turn on your Kobo Vox I suggest that you contact Kobo and ask for assistance regarding the problem.
Also, I found this website that teaches a fix to that kind of problem. I'm not sure if it works. (*****Do it at your own risk*****)

1. Take the back off the Vox. Use a fingernail, or something thin to pop off the plastic quilted cover.
2. Gently remove the battery. This is the large, thin rectangle taking up most of the left hand side. The battery is attached to the Vox with a small cable, emerging from the bottom right hand corner of the battery. This step makes it easier to access the cable plug.
3. Grasp the small white plug at the end of the cable. Gently wiggle it while pulling, to detach it from the Vox.
4. Once you have unplugged the battery, plug it in again, making sure you feel a “click”. If you don’t feel the click, try again. The plug is not properly seated, otherwise.
5. Place the battery back in its compartment, ensuring you loop the wires under the tab at the bottom of the battery housing, so they don’t get pinched.
6. Snap the back of the Vox back into place.

Again, I remind you, do it at your own risk.

Source: Link