My Compaq Laptop Turns off when charging cable unpluged...

Hello, my laptop turns off automatically when i disconnect its charging plug...
first time it happened 2 or 3 days earlier when i was working and when i unplugged the cable from socket... my laptop turn off at that movement ..... then i tried to start it but it does not...... and still it does not starts without ac power......
i dont think that the battery is dead..... and now i m not understanding the problem plz help me........