I would choose a different location to unpack the files. Can you tell us the exact name of the StarOffice file you downloaded with extension and all? This would help to determine the necessary steps from beginning to end. Also, I have read that having OpenOffice already installed can be troublesome when trying to install StarOffice. Do you know if you have OpenOffice installed? If so, you may want to uninstall it first and then try the StarOffice installation routine.
The way i would approach this process is as follows - starting from the very beginning:
-As normal user with desktop environment running (i.e. kde, xfce, etc..), start a terminal.
-Change directory to your users Desktop directory: cd Desktop
-Make sure your StarOffice8 package is in this directory (because this is where you have it stored, correct?): ls -al
you should see it in the listing
-Switch to root: su
-Enter root password when prompted
-Unpack the StarOffice package (if necessary) as suggested by rbistolfi
-Change into the unpacked directory (if one is created): cd /home/us/Desktop/name_of_SO8_directory
-Execute the script: sh so-8-pp8-bin-linux-en-US.sh
-Choose a different directory when prompted: Select the directory in which to save the unpacked files. /home/us/Desktop/name_of_SO8_directory/setup_SO8
-You should not see any errors during this process (i.e. cannot create directory, No such file or directory, etc..)
-Change into the unpacked directory: cd /home/us/Desktop/name_of_SO8_directory/setup_SO8
-Execute the setup script: ./setup
-Exit root: exit
If the installation was successfull then you should have presented with some kind of GUI installation routine that _probably_ indicated that things were installed successfully. You should then be able to run StarOffice with the correct terminal command (maybe 'soffice', 'staroffice', or something similar).
HTH and Good luck!