Daily, I take my MBA to work, and connect it to my 30" cinema display. At the end of the day I disconnect and take it home. Once back home, I plug into the 24" LED display and keep on working. The MBA sleeps while I'm cycling to and fro — and wakes up when I plug it in.
Today, I got home, plugged in, and found a blank screen. I waited; nothing happened. I waited some more. Eventually I gave up waiting and did a forced shut-down, by pressing and holding the power button.
To restart, I pressed the power button. The chimes, and the apple came up just as usual; then the little wheel thing came up, but it didn't move. I waited — nothing. I plugged in, unplugged, opened. closed, shut-down (again) etc. I tried all of this again, and again, in various permutations, and with plenty of waiting — nothing. Frozen as a dead parrot!
So, I reset the System Management Controller — that worked :-)
To reset the SMC: Shutdown; plug in to mains power; hold down shift-ctrl-alt (alt is aka option) on the left side of the keyboard, and press the power key once; then release the keys, wait 5 seconds, and press the power key to restart. Effective magic!
The SMC includes the Power Management Unit (PMU) you may be familiar with from other devices.