You were using this guide, correct?
If the battery works, and the AC charger works, the most likely problem is that you didn't reconnect the battery correctly (Step 3 in the guide). Open up the computer, unplug the battery cable, check to see that all the pins in the connector are straight, and reconnect the plug securely.
If that doesn't work, it's possible that all the moving around that happened as part of removing the display knocked the keyboard connector loose. The power button connects to the motherboard through the keyboard ribbon cable. Although the keyboard is not disconnected as part of the Airport replacement, it's close to the left RAM slot as you look at the back of the motherboard. Step 12 of the MacBook Pro 13" Unibody Mid 2010 Upper Case Replacement guide shows the location and connection method for that cable.