You could try powering it on without the battery installed, some people have had success with that, others seem to have been able to get it to power up by doing an SMC reset with the power and battery removed, others seem to have had success getting it to power on without the battery by unplugging the power and battery, holding down the power button, then plugging in the charger...I'm sure others have even tried voodoo.
But without knowing more, and the fact that it did power on for you at some point, does make me lean towards it being a bad battery. I'd hate to tell you to go out and spend money on a part that won't solve your problem, so perhaps someone else will chime in and confirm what I've said or offer up another suggestion.