There are a couple ways you could tackle this. First, in Analysis, you could use the Active Project Search and change the filter settings to Inactive (and maybe Closed) or Both Active/Inactive and Open/Closed. The results would return and you could click on any project name to see the details, including the Briefcase and Feed.
Second, you could create a Project Report either in Analysis (+New > Report > Projects Report) or in the Projects Application (+New > Report > Projects Report). If you did not add any filters to the report, it would return all projects. You may consider limiting to just inactive or completed, however. Keep in mind, if you run this report within the Projects application it is limited to the project to which you have access (as a manager or resource).
Finally, if you go to the Projects application and click on Manage Projects, you could view the inactive projects that you managed.
There's more than one way to address this. I think the reporting options are the best approach. Let me know if you have further questions.
Director of Client Services