If you encounter Project Server Queue Jobs aren't processed anymore or the Project Server Queue Service doesn't start anymore it might happen that the Account with whom you are running the Project Queue Job doesn't have enough permissions on the SQL Server or you have changed the account recently or the accounts password has been changed (in this case you would have to reenter the password and restart the Service job). This is why normaly it would be convinient to have an account set up (the one with which you are installing the Sharepoint/Project Server) to run the services and also to have the Password never expired option enabled.
To check if the service account that is running the project queue still has permissions to access the SQL server it is common to test this by creating a SQL UDL file and test the connection.
1) Create a new empty text file like "test.txt" (For example, right mouse click on an empty place on your desktop, select "New" and "Text Document")
2) Rename the file as "test.udl"
As soon as you renamed the file, text file icon should change to a UDL icon
3) Double click on test.udl file and you'll receive a window titled "Data Link Properties"
You'll get all the installed OLE DB Providers on the box when you've switched to the Provider tab. If the OLE DB Provider for the database/datasource you're interested in is in the list, select the OLE DB Provider and click on "Next"and you'll switch to "Connection" tab and will be ready to play with the OLE DB Provider. The rest depends on the OLE DB Provider you selected.
For example if you selected "Microsoft OLE DB Provider for SQL" , you'll see a window like that :
You'll need the name of the SQL Server (or instance name) you're trying to connect to the textbox in the 1st part. "Use a specific user name and password" is selected by default in the 2nd part and this means "SQL Authentication". You'll need to enter a the account that is running the project server queue job service username here.
If you select "Use Windows NT Integrated security" radio button, then the Username and Password textboxes will be disabled and the credential that you logged on to the machine will be used while connecting to SQL Server. Be sure that your SQL Server is in "mixed" mode (Please refer to SQL Server Books Online for the details )
You can either click on "Test Connection" directly to test the connection or click on the combobox to enumerate the available databases/catalogs on the server.
If you click on "Test Connection", you should receive "Test connection succeeded" message if you can connect to the SQL Server :