All keys work but Power Button

After popping off the bottom cover carefully short across the power pads which are near the keyboard ribbon cable. They are the two square solder pads circled here:

Here you want to emulate holding the power switch to force a system to shutdown. Then disconnect the battery after which you'll want to pull the keyboard ribbon cable (review the steps in the IFIXIT guide below). Using an external keyboard & mouse/trackpad (USB or Bluetooth) reconnect the battery and now using the pads start the system up as you don't have the internal keyboard & trackpad working (disconnected) use the external keyboard & mouse to test things out. Shutdown the system from the menu is it staying shutdown?

• Tip: using a small piece of electrical tape create a pull tab to stick on the ribbon to help in removing it and also re-inserting it. Don't forget releasing the catch and relatchng it afterwards! And don't break it, it's very delicate!

At this point you'll likely need to either try cleaning the keyboard or replacing it. Follow this IFIXIT guide: MacBook Air 13" Mid 2011 Upper Case Replacement it will get you mostly there. Here's a YouTube vid on it: Replace liquid damaged keyboard of 2011 Apple Macbook Air. Lastly, here a link to what you can find on eBay: MacBook keyboards. Get one with the extra rivets as you will likely need them.