Richard,

I had the same problem with a setup similar to yours although I've seen this on other Macs with Panther. The solution is simple.

1. Go to your desktop and make sure nothing is selected.

2. Go to View > Show View Options (Command-J) and click on "Snap To Grid" near the bottom of the window. Now arrange your icons as you'd like them to appear every time and they should stay that way from here on out.

You should now be able to shut down, sleep etc. without any change in your desktop icon arrangement.

Unfortunately, you don't seem to be able to select "wide" or "tight" grid arrangement the way you could in OS 9 and below, so you're stuck with whatever grid positions appear. The only way to customize this is to use the same View Options dialog from step 2 to change the size of your desktop icons.

Pat