The most basic cause of a problem like this is an error when creating the package. Check through the package again carefully looking for things like the execute date/time and expiry date/time, the operating system/processor type selected, the path to the executable etc. Failing that, what version of SMS do you have and on what operating system?
You're right; the package simply calls a script - usually a batch file - that runs whatever installation procedure is required. The name of the script and the path to it is one of the parameters you supply when building the job. Remeber that you also need to distribute the package to the SMS servers on your site(s). Usually we do this in two stages: First we create a job that only distributes the package but doesn't attempt to install it and watch to see that complete. Then we create a second job with the distribution options unticked and all the client install options specified. Have a look in the SMS share (usually SMS_PKGD) on your central SMS server for the highest numbered (and therefore most recent) package. If you look in there you should find the batch file plus all the required files for the installation. Sanity check that, and maybe try copying it to a PC and making sure it installs manually. If that's okay then check on all your other SMS servers (if you have multiple servers) that the same package is held there