DW is a good tool. Do you also keep Drive Genius in your tool box?
It's another great utility I ran across a coupla years back.

Too many utilities, so little time.

As far as repair and recovery DiskWarrior and FileSalvage do what I need, but DriveGenius does put a lot of tools in one spot. I don't see a data recovery though with it. Its repair is DiskUtility from the looks of it.

I've checked out the demo. Most of the tools are free already, but it's all together and does have three non free solutions that I know of. The Integrity check looks like it might stress the drive nicely, for an enterprise solution that would be handy to ensure integrity of the drives, and the defrag would be handy but I have iDefrag. Bad block scan looks handy sort of, but my rule of thumb is if the symptoms point to a bad HD, it probably is bad, and for the cost nowadays I just replace it.

As far as Sector Edit, too geeky for me.

Between DW and TTPro, I'm covered.

And us.

I started up with the Mac OS-DVD, went to the Disk Utility program, did a complete check up of my HD, I controlled and repaired my HD. It was no problem, fully repared, it said. Afterwards I could indeed restart the computer once when my Mac OS dvd was still in the computer. When I pulled out the DVD I could'nt restart (or turn off) the computer anymore again. I always have to use the button on the back to turn of the computer.
I do have some weird documents in my Trash, 3 documents, no extention, when I clic on "More info" they disapear from the trash. I can not drag them to the desktop either. When I put something new in the Trash, you see those 3 documents again. They look for example like this 3ZÂ~%NE.K< or lt6ûåó?.xêä
Very strange. Can this be the reason of my problems?

At this point, I'm thinking maybe there is some directory damage. Do you have access to Disk Warrior - recent version?

I wonder if Windows is installed on it either via Bootcamp or virtualization?

Good question.

I'm assuming that the machine behaves normally other than the shutdown/restart problem. I wonder if there is a process that is refusing to quit.

I do have some weird documents in my Trash, 3 documents, no extention, when I clic on "More info" they disapear from the trash. I can not drag them to the desktop either. When I put something new in the Trash, you see those 3 documents again. They look for example like this 3ZÂ~%NE.K< or lt6ûåó?.xêä
Very strange. Can this be the reason of my problems?

Hold down Option while selecting "Empty Trash" forces a "Force Empty Trash" scenario.. this may dump those files.

You may also look into Cocktail or a similar program for doing routine maintenance.I would recommend running this first. It has a trial period.

http://www.maintain.se/cocktail/index.php

Force emty trash doesn't work with those files. they stay in the Trash.