Here are the steps you need to take in order to reuse an old project:

1. Copy the entire folder that contains your older project and all associated files.  Then paste it into a new location on your hard drive.  Next, rename the copied folder and give it a new name.  If you do this kind of thing frequently, you'll realize that it is best to have your folder structure set up so that your installation project and all files necessary to build it are in the same folder structure.  This makes copying and reusing projects an easy affair.
2. Now, open the "copied" project in InstallShield.
3. Go to the General Information group, Summary Information Stream property sheet, click the Package Code, and click Generate GUID.
4. Go to the General Information group, Product Properties property sheet, click the Project Code, and click Generate GUID.
5. Go to the Organization group, Components view, and click each component.  Then click the Component code property, and click Generate GUID.  Do this for all the components in your project.
6. Go to the Media group, Path Variables view, and change all the paths to point to their new folders.  Currently, they point to the folders associated with the original project, and you don't want that.
7. Make any other changes necessary to make this a different project.  For example, under General Information view, Product Properties, change the Name, Version, INSTALLDIR, etc.
8. Rebuild and test.

When you copy and reuse an old project, the critical things you need to change are the GUIDs in your project and the Path Variables.  Yes, you need to change other things, but these items are critical.  If you don't change all the GUID values, your new installation project will conflict with the older installation project when they are both installed on the same machine.  This will cause you a lot of grief and calls and emails for tech support with your customers.

Finally, even though I shouldn't have to mention this, whenever you do something like this, you have to test throughly to make sure your new installation works as you intend it to work.