Macbook Air won't restart until I disconnect the battery

I have a mid 2011 13 inch Macbook Air. If I shut down the computer it will not restart unless I open the bottom panel and disconnect the battery for several seconds. The battery is fully charged. Reseting SMC did not help. After disconnecting and reconnecting the battery, the laptop will start up fine and work until it is shut down again.

Any ideas what the problem/solution is?