You need to somehow get into Finder. Perhaps click at one of the screen edges (a few seconds of moving the pointer there will do), or use an application launcher (e.g. Quicksilver, LaunchBar). If you never disabled the keyboard shortcuts, press Ctrl-F3 once to get Dock keyboard focus, then Return.
Cmd-N to open a new window
Cmd-Shift-C to get to top (machine) level
- Press
Esc, then type Volume Name once to get the desired entry
- Press
Cmd-E for Eject
If you have mounted disk images on external volumes, this might not work at all, they block ejecting.
If you don't know the volume name, replace steps 3 and 4 with:
- Press
Esc, then Down once to select the first list item.
- Press
Cmd-E for Eject
- Select another list item by pressing
Esc (clearing selection), then Up or Down once or more.
- Repeat these steps a few times to unmount all volumes except the ones you cannot (i.e. Network item and your start volume)
Alternatively, find out your exact umount command and start Terminal using an application launcher, or by finding Finder like above, then pressing Cmd-Shift-U to open the Utilities folder, then type Terminal to locate the program, then Cmd-Down to start it.
If you have a launcher such as Launchbar, type your hotkey then "shutdown". Press enter and see if the machine gets turned off.
Close the lid to go to sleep. Not a dismount, but there shouldn't be any more disk activity.
Click the very top left of the screen to open the Apple menu (move the pointer for a few seconds there), or, if you didn't disable the keyboard shortcut, press Ctrl-F2 then Enter to focus the menu bar, then open the Apple menu. Press Up twice, and then Option+Enter. This will shut down the machine.