If your machine has a PRAM backup battery (12-inch models generally didn't) you might try to get some charge into that battery by leaving the computer on the power adapter overnight with the main battery removed. Unfortunately, there is no easy way to test whether the power adapter is really working properly other than to substitute a known, good adapter. If the battery is completely gone, there is no charging going on and the computer will cause the indicator to go to green, just as if the battery has been removed from the computer. There is always that possibility, but the charge indicator is coming from the computer.
the charger shows the green (amber) light when plugged in despite of that are there any chances that the charger mite be faulty? Nonetheless, do the reset at least once, following the instructions exactly. It may do no good because if you do not have a good battery or backup battery going in the machine, the PMU may have problems initializing. You should do the PMU reset if you haven't done so already. I tried to start it without the battery just with the charger on but still no signs of life it is not powering up only so there is no question of going to the PMU reset. It is not uncommon for the main batteries to crap out after a few years I had one die a painful death at five years while I have two that are doing fine after eight years, actually one of them is "good as new" or better. That is to say, if it's a G4 PowerBook, it's old.
You don't specify which model (look at the bottom case for an A# number, like for instance A1025, from which we can get more specific about things) so basically the G4 PowerBook is between five and ten years old. If you don't get any lights, then the battery is probably completely gone. The problem is none of the lights on the battery go up when i press the button.