Hold down the power button for about 10 seconds, and then try powering it back on. Sometimes Apple laptops with near-dead batteries will get stuck in a sleep state, and it's necessary to kill the power.
If that doesn't work, unscrew and take off the bottom casing, disconnect the battery, and see if your machine powers on with the battery disconnected. If it does, power off and reconnect the battery and power the machine on. You're most likely fine. If it doesn't, you've got bigger issues.