Argh! Last night, I was laying in bed with my iBook, and I unplugged it to have it rest on my legs. What happened was, it went into sleep mode because it seemed that the charger wasn't working (this is an offbrand targus charger) So I plugged it back in for a while and let it charge. After a while, I unplugged it again and it went back to sleep again. I tried this another time, and it seemed that it had just one sliver of power left. So, I plugged it back in. Then a little bit later, I moved a bit and the plug fell out, and my iBook just shut off. It was late, so I left it that way, plugged it back in, made sure the battery led was blinking to show charging, and went to sleep. I think this morning I saw that the leds were off, and I ignored that. Then when I got back home maybe 7 hours later, I got my iBook out and tried to turn it on, but I get nothing. So, I plugged it in with the Apple charger, and it's just about all the way charged, and it's STILL not turning on. Please help

Try resseting the power control unit, if you have another mac run a search in mac help for reset power or something like that, or you can try the apple suport web page to find the exact instructions on how to perform the reset.
good luck

I did the PMU reset already, and I also tried to turn it on without the battery

Try: Command-Control-Power. If they shut off while sleeping, its often the fastest way to bring them back.
Also try unplugging, removing the battery and leaving it for a while. Half an hour or so should do. Then plug back in (AC only first, then try battery only, then both) and see if it boots.