MacBook won't turn on unless connected to the charger

Hey, Ive got this problem with my MacBook (Intel-Based), and basicaly what happens is that, If i try turning my MacBook on while the charger is not connected to it, the white light just flashes once and then the macbook turns off. But everything works fine if the charger is connected (Only all the applications seem to be a bit slower).
Thanx for any help

When the power cord is plugged in, what does the battery charge icon indicate?

If it is charging then it shows a blank battery with this thunder-bolt icon and it also sows the percentage... everytihng seems to be working fine though.