Never mind, it turns out I was doing a lousy job looking for a guide the first time. I found this, which describes exactly what I need.

However, my problem still persists. After I turn my phone off, it will not come on by pressing the Power button or by plugging it in the PC. The only thing I can do is plug it in the charger.

To get the green light, I need to:

1. Turn the phone off
2. Wait a bit
3. Press and hold the Volume Up (or Down) button
4. Plug in the charger
5. Wait until the LED light up red
6. Very quickly swap the charger cable for a USB cable from the PC
7. Wait until the LED turns green (it flashes first, until it turns steady green)
8. Release the Volume Up/Down button

However, at Step 7, the phone has already booted up to the "battery charging" screen. I assume that is the problem.

So I guess the real question is, how do I fix my battery problem?
It looks my phone does not like the "20%" thing.