Project Center cannot access the project(s) you're trying to view. It is mostly likely that you either don't have permissions ...
If a timeout error occurs when Project Server is trying to get data to display the content of the Project détails view, you can see in the ULS log the following information:
PSI: PWA.ProjectGetProjectDetailsForGrid SqlException occurred in DAL:
<Message> System.Data.SqlClient.SqlError: Timeout expired. The timeout period elapsed prior to completion of the operation or the server is not responding. </Message>
When you trace with SQL Profiler, you detect a specific query takes a lot of time to be executed.
If you extract this query, you execute it in a new query against the Published database and you display the Execution Plan, you detect the main Cost% comes from Seek command on different tables with clustered indexes.
This means the root cause of the timeout is certainly due to a high fragmentation of indexes on these tables.
In general, it is strongly recommend to create a Maintenance plan on Project Server databases.