Differentials are based on the previous full backup. If you do not have the last full backup that ran before the differential, you cannot use that differential backup.

If you have an unbroken chain of log backups since the full backup that you have, you can restore the full and then restore the logs in sequence.

If you do not have a full and unbroken log chain, then you cannot restore to the latest point.

Can you be more specific about what backups were taken and which ones you have available?