Maybe a script like this would help you find the most recent backup and it's path:

select top 1 bset.database_name, bset.Type, media.physical_device_name, backup_start_date

from msdb.dbo.backupset bset

join msdb.dbo.backupmediafamily as media on bset.media_set_id = media.media_set_id

where database_name = 'Database_Name'

and type = 'D' -- Full

order by backup_start_date desc