Some more ideas:

1. is to - once you've managed to shutdown, to remove the power cord and battery. Wait a minute or two, and then try to cycle your system (start/stop). This can reset the Power Management Controller.

2. Create another user account. Log in only as this test account. If you don't have the problem, it's likely to be something in your user software. If you do have the problem, it's possible it could be hardware.

3. Try to recreate the problem just using battery power.

4. Follow the steps for Apple's System Management controller -

Resetting the System Management Controller (SMC) Resetting the SMC on Mac portables with a battery you can remove

Shut down the computer. Disconnect the MagSafe power adapter from the computer, if it's connected. Remove the battery. Press and hold the power button for 5 seconds. Release the power button. Reconnect the battery and MagSafe power adapter. Press the power button to turn on the computer.

Some more ideas:

1. Create another user account. Log in only as this test account. If you don't have the problem, it's likely to be something in your user software. If you do have the problem, it's possible it could be hardware.

2. Try to recreate the problem just using battery power.

3. Follow the steps for Apple's System Management controller -

Resetting the System Management Controller (SMC) Resetting the SMC on Mac portables with a battery you can remove

Shut down the computer. Disconnect the MagSafe power adapter from the computer, if it's connected. Remove the battery. Press and hold the power button for 5 seconds. Release the power button. Reconnect the battery and MagSafe power adapter. Press the power button to turn on the computer.