sheesh 0 Newbie Poster

I have a latitude d600 laptop that periodically won't turn on when the adaptor is plugged in and when the battery is charged. Sometimes it does and sometimes it doesn't. Last night it was working fine, but when I woke up this am it was off. Tried turning it on, and no go. Battery looked dead (even though it was plugged in) so unplugged and replugged it in. Battery started charging and eventually showed full charged lights on battery. Tried turning it on again without battery, and no response. Tried with battery and no adaptor, and no response. Tried with battery and adaptor, and the battery charge light flashes but no other response. Any advice?