SQL Server restore full backup + partial differential backups
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.