During a thunderstorm, the power flickered off for an instant with the GPX D1816 in standby mode (red light?), but now the standby light is blinking green and it will not work.

If the indicator light is blinking it is probably a faulty power supply. I just fixed mine today. Open the player up by removing the Phillips screws and locate the power supply board - this is the circuit board that connects directly to the incoming 120 Volt power. On this board look closely at the barrel shaped capacitors and note any bulging at the top of these capacitors. My 1000uf 16volt cap was just barely bulging so I decided to replace it with a piece salvaged from an old PC power supply. It is simply a matter of de-soldering the old piece and soldering in a new one. If you must purchase one you could probably get one from Radio Shack or Digi-Key for under a dollar. The replacement should be 1000uf and rated for at least 16volts or more.

Unplug it and and plug it back in, if that doesn't help then leave it unplugged for a couple of hours, over night if possible, then plug it back in and see if it resetted itself, it it does the same thing then there if an internal failure of the device.