MacBook 1,1 wont power up when it runs on the battery.

Hi There.
My MacBook's battery ran out a year ago, and then I bought a knew one, but it might be an apple copy battery, cause it did not fit entirely into the machine, but we're only talking mm here! It works fine for almost a year, but the suddenly the computer could not power up when only on battery, and if i remove the power supply my mac powers down immediately. The wired thing is that my mac seems to believe that the battery is in fine condition, and when I push the button on the back of the battery(the one that shows charging level) they light up. Even more wired is it that my Mac stays "alive" if I just put it to "sleep" before removing the power supply. But it powers down if I lift the screen to "wake" it up again.
I hope someone can help find out what's wrong!
jo

Try (or buy) a known-working original Apple battery... these 3rd party chinese copies are horrendous in my opinion - always a cause for problems.