It charges with the comptuer on or off, makes no difference, as long as it is plugged in.
As for your CD's, your comptuer shippped with OS X 10.5.7, and the grey CD is just that, the Snow Leopard disk is Mac OS 10.6. Each major release of Mac OS is a by-purchase-only product, and goes 10.0, 10.1, 10.2 etc. etc. so 10.6 is the next major release. It hit the market about 2 weeks ago. I would put this in and install it immediatly, its much easier to be able to just wipe your comptuer and "start fresh" before you start putting documents on it and such, because then you'll have to back those up before installing.
Also your "applications CD", I don't think it will have anything different on it. . . anyone else know what might be on the CD? Your other option is just to put it in and see what it has.
Sounds to me like something went bad, I honestly don't know what. If I were you I would PLUG IN the laptop, (make sure the cable is plugged into the laptop and the wall), then start the installation over, tell it to erase and to a clean install on the HD.