HI Brett,
The privileges listed in the SPC wiki for Ubuntu 10.04.3 (
http://tools.proteomecenter.org/wiki/index.php?title=TPP_4.5.2:_Installing_on_Ubuntu_10.04.3) tpp/data directory has them set at 771 and the owner and group set to the user that Apache runs as in my case its www-data for both. I don't think its necessary to set the data directory to execute so 660 (e.g. chmod -R 660 /your_path_to/data) should also work. If that isn't the problem check your tpp/cgi-bin/
tpp_gui_config.pl file and see if it is correctly set for the path of the data directory.
Note that in the above wiki entry we are installing in /usr/local/tpp. Yours seems to be in /opt. Either should be fine as long as you correctly specify the paths where you have TPP installed.
Thats all I can think of now.
Brian