The fact that the library re-indexes when you make this change suggests you are not copying all of the required files to the new PC. It also suggests there are issues with the changes you've made on the original PC. To test this on the original PC you can delete the sysindex.cbf file in the library folder (take a backup of the entire library folder and sub-folders before hand). This will force a re-index and log the issues with the current library. As the details you provide are brief it is difficcult to draw any conclusion as to the cause.
If you want to share libraries across projects move the library to a common shared drive. The idea behind the Starter Library is to get you up and running quickly after installation, but it is not intended to be used as your permanent library if installed in the software tree as it will be replaced at each version of software. You should choose a common shared location and either copy the library there or create a new library and use Library Services to move data across from the Starter Library.
If you are still stuck contact your local support.
Thanks for your reply. Actually I don't really know what I'm doing with this program and I wasn't sure the best way to copy an existing one. I used the starter library to play around with and then planned to create a common shared library, but thought to try first to copy the library onto another PC. My method of copying was to copy the entire folder. Anyway the attempt was less than successful and took some time to repair on the new PC so I assumed that there was a better way of working and so I'm happy to get some reply here.
The correct procedure to copy a library (as I understand from your email) is to create a new library and then copy data from the old one to the new one using library services. When I have some time I will try it and will let you know if it is more successful.