Yes, I also had similar problems when attempting to do such a thing. For additional modules do:

pp -M this::module -M that::module -o out.exe foo.pl

... and I believe in reference to your last question you must include two things:
- a similar folder name of the my_script.pm (module or script) you want to import as it appears in your @INC using -I
- and also add the script using a full path name using -M.

pp -I \another\folder -M some::module -M c:\full\path\my_script.pm -o out.exe foo.pl

Note: I'm never done this way of -I although I believe its the solution and will be attempting on the next PAR I do

Also, I'm not sure if in writing the command in any particular order is important but I'd suggest doing -I before -M just in case.

Additionally, if you don't create the additional folder in the archive using -I it will drop your own my_script.pm that you imported using -M into the root of the PAR archive. Although this isn't probably the cleanest way to pack the archive, I found for my programs (EXE's) it still finds the my_script.pm because it must search this root folder of the archive for included modules/scripts.

Also, the PAR archive is really a zipped archive which can be viewed in Winzip. If you create the PAR file without using the -o flag like this:

pp -I \another\folder -M some::module -M c:\full\path\my_script.pm foo.pl

... and then open the resulting PAR file in winzip you'll get an idea of the structure and setup of the PAR archive. Hope that helps.