After trying all other suggestions I could still not get into the boot menu. Only flickering. The battery-cable was not loose, but the battery was probably completely empty. After many attempts, I noticed that if I kept the Nexus 7 disconnected for a few minutes. Then connected the charger and press power immediately it would show the Google boot screen. Now you should get into the boot menu if you press the volume down quickly enough. If you weren't fast enough, you have to disconnect and wait a few more minutes before trying again.
See here for instructions after you get into the boot menu: https://support.google.com/googleplay/answer/2668668?hl=en