DBNETLIB][ConnectionOpen (Connect()).]SQL Server does not exist or access denied

After moving a package to another server, I am unable to run it from a stored procedure using xp_cmdshell or from a job. The package exists in the file system, and I added it to the SSIS Package Store. If I run it in BIDS it runs. If I run it from the package store it works. As soon as I try to run it from the job or the stored procedure, I get the following errors:

Error: 2016-02-11 15:10:29.80   
Code: 0xC0202009  
Source: Package Connection manager "MyServer.MyDB"   
Description: SSIS Error Code DTS_E_OLEDBERROR. 
An OLE DB error has occurred. Error code: 0x80004005.An OLE DB record is available.  Source: "Microsoft OLE DB Provider for SQL Server"  Hresult: 0x80004005  Description: "[DBNETLIB][ConnectionOpen (Connect()).]SQL Server does not exist or access denied.".
End Error
Error: 2016-02-11 15:10:29.80   
Code: 0xC020801C   
Source: Data Flow Task OLE DB Destination [39652]   
Description: SSIS Error Code DTS_E_CANNOTACQUIRECONNECTIONFROMCONNECTIONMANAGER.  The AcquireConnection method call to the connection manager "MyServer.MyDB" failed with error code 0xC0202009.  There may be error messages posted before this with more information on why the AcquireConnection method call failed.
End Error
Error: 2016-02-11 15:10:29.80   
Code: 0xC0047017   
Source: Data Flow Task DTS.Pipeline   
Description: component "OLE DB Destination" (39652) failed validation and returned error code 0xC020801C.
End Error
Progress: 2016-02-11 15:10:29.80  
Source: Data Flow Task    
Validating: 100% complete
End Progress
Error: 2016-02-11 15:10:29.80  
Code: 0xC004700C   
Source: Data Flow Task DTS.Pipeline   
Description: One or more component failed validation.
End Error
Error: 2016-02-11 15:10:29.80   
Code: 0xC0024107   
Source: Data Flow Task   
Description: There were errors during task validation.
End Error
DTExec: The package execution returned DTSER_FAILURE (1).

Both the SQL Server service and the SQL Server Agent service are using the local system account to log on. I have changed the creator name and creator computer to the production server it has been moved to.

This is the connection string from my package:

Data Source=MyServer;Initial Catalog=MyDB;Provider=SQLOLEDB.1;Integrated Security=SSPI;Auto Translate=False;

Thanks you in advance for any help you can provide.