my finder windows disappear after a restart

Copy the line of text below, including the ~ at the start

~/Library/Preferences/com.apple.finder.plist

Right (ctrl) click it & choose Services - Reveal. A finder window should open, with that item selected. Trash the file, then immediately relaunch Finder, or log out/in.

That contains the preference settings for Finder. If there's no change, you can use Trash - Put Back, choosing Replace at the 'newer version exists window' then relaunch/logout as before.

Failing that, try Safe mode, as Eric suggested.

You can also try booting into the Safe Mode using your normal account. Disconnect all peripherals except those needed for the test. Shut down the computer and then power it back up after waiting 10 seconds. Immediately after hearing the startup chime, hold down the shift key and continue to hold it until the gray Apple icon and a progress bar appear. The boot up is significantly slower than normal. This will reset some caches, forces a directory check, and disables all startup and login items, among other things. When you reboot normally, the initial reboot may be slower than normal. If the system operates normally, there may be 3rd party applications which are causing a problem. Try deleting/disabling the third party applications after a restart by using the application un-installer. For each disable/delete, you will need to restart if you don't do them all at once.

Safe Mode

Safe Mode - About

You're welcome. There may be an obscure preference key that was set to off, although it wasn't one that I could quickly uncover. NSQuitAlwaysKeepsWindows didn't seem to have any effect here, so presumably is for later OS X versions.

Does another user account show the same problem ?.

Mac OS X 10.6: Creating a new user account