Battery on G4 had failed, and would only hold a charge for 5-15 minutes. After using it this way for around a year (keeping it plugged in to the wall) it finally stopped powering up/charging unless i had the plug on the laptop positioned in the perfect position. This required a delicate balancing act of placing the plug on a book etc. and leaving the laptop hanging off in order for the charging light on the plug to go green. Eventually it stopped charging/working all together. After removing the bottom cover and metal shield I noticed a small spot on the chip of the DC inboard (though at the time I wasn't aware that this part was called the DC Inboard) that appeared burnt or darker in color than the rest - see attached photos. It also had a faint smell of burnt wiring. A google search landed me on the ifixit.com page where I found the exact part i was looking for. I wasn't sure if this would fix it or not, but figured for $30.00 it was worth a shot.
The repair was very straightforward and easy. I left my laptop partially apart until the part arrived. After receiving the part, the repair took only 10-12 minutes. The computer came back to life after 3 or 4 months of sitting dead.
Attached pictures are of the old DC Inboard for reference. Hopefully they help in your diagnosis. Notice the very small dark circle above-left of the TEST/OK sticker.