My Google Glass does not start up When I try to turn on my Glass using the Power button, the power LED turns on for a second, but then turns off. I can tell that my LCD is working because when I try plugging the charging cable in, I see the battery icon displayed on the screen. However, once I try to turn it on, it doesn't start up, even with the charging cable plugged in.

Is there a battery issue or is it something wrong with my firmware?

Note that this is different from Google Glass Stuck at the “Glass” screen, as that question manages to make it to the Glass splash screen, but in my question, it does not even make it there.
Offhand, it sounds like your battery is still too low a charge to actually turn on. Make sure you leave it plugged in and the LED is on or pulsing. Do not turn it off while charging.

If you're still having problems, your best bet is to contact the support team.