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If that doesn't work run the hardware test utility that came with your machine.
If you are going to do this, you should run the extended tests and place the machine in LOOPING ON mode. You can do this by pressing Control+L on the testing screen. Let the tests run overnight, and when you come back in the morning, you will either see an error message or not. If there is no error message, you restart your Mac knowing that it's unlikely that a hardware failure is causing your problem.
Jonathan S. Abrams, CEA, CEV, CBNTVice-Chairman, NY section, AESApple Certified - Technical Coordinator (v10.5), Support Professional (v10.6 and v10.7)
It might be worth testing this problem with hardware peripherals unplugged. Hard drives, recording interfaces, USB accessories. Try removing one them and tell to shut down. Perhaps one of them is causing this? Do it one by one so you could potentially nail down a specific device.
Also did you try another user account, as previously suggested?
You could also open activity monitor to gain a little insight as to what processes are running. Maybe you can identify something unwanted? Or taking up too much CPU?
I've tried logging off before shutting down. I really only have one account on this computer. Will create a new one and give that a try. (Not expecting that to work, but would be thrilled to be proved wrong.) The hardware test didn't find any issues. Thanks for the suggestions.