SQL Server restore full backup + partial differential backups I created a full backup of my database using SQL Server Management Studio wizard, and then I perform differential partial backup each day via cmd to the same file. 

SQL Server version is 2008 R2.

Here is the command I use to perform backup:

BACKUP DATABASE [db_name] 
TO DISK = N'path_to_backup\db_name.bak' 
WITH DIFFERENTIAL,  
     DESCRIPTION = N'Differential backup of the staging database', 
     NOFORMAT, NOINIT,  
     NAME = N'db_name-Differential_Backup', SKIP, NOREWIND, 
     NOUNLOAD, STATS = 10 
GO


I can't figure out how to restore the entire database (full backup and all of the partial backups).

I tried restoring full backup with NORECOVERY and PARTIAL options:

RESTORE DATABASE [db_name] 
FROM DISK = N'path_to_backup\db_name.bak' WITH 
FILE = 1,  
  MOVE N'db_name' TO N'path_to_sql_server_installation\MSSQL\DATA\db_name.mdf',  
  MOVE N'db_name_log' TO N'path_to_sql_server_installation\MSSQL\DATA\db_name_1.ldf', 
  NORECOVERY, PARTIAL, NOUNLOAD,  STATS = 10
GO


This works ok, but then I try to restore the partial backup using the following command:

RESTORE DATABASE [db_name] 
FROM DISK = N'path_to_backup\x12parsedb.bak' WITH  
FILE = 2
GO


This also completes without errors but it overwrites the data from the full backup and I'm left with only small fragment of data that was in this partial backup.

All of my backup data is stored in a single file, and there are around 130 partial backups.

I've tried to use Management Studio wizard but the result is the same.
Not sure what you expect from partial backups, but they are only useful for read-only filegroups:


  partial backups are designed for use under the simple recovery model to improve flexibility for backing up very large databases that contain one or more read-only filegroups.


Differential backups are a different story, but they are not used as you use them. They are supposed to speed to up a full restore by skipping over some log backups, not as a replacement for full backups. 

Is rather unclear what you actually have. I guess you have a full backup and 130 differential backups. In such case you can restore the original full and then apply the last differential.

My suggestion is to implement a correct backup plan (full recovery mode, periodic full backup and frequent log backups). There are many examples how to do this. Start with reading Introduction to Backup and Restore Strategies in SQL Server. Go over some tutorials like the ones from SQL Server Backup
Best Practices and Articles. Understand what you're doing, don't guess.