Funnily enough, just last week I wrote a little howto on this (see my website in my signature for more info). The reason for the problem you're experiencing is that while most *nix distributions work fine when the setuid bit on a binary is turned on, the distributions specifically disable the use of setuid bits on shell scripts, due to their insecure nature.

There are two possible workarounds: a) edit the sudoers file so that sudo doesn't require a password for the commands that you need to execute in your shell script, or b) call the script from a C program using the system() call.

Thank you very much for your help! I will check if it works later, but I think it will. Thanks!