What account are you running the SQL Server engine under? Does that account have access to the location of the backup file.
Check out this post on SSC with the same issue.
http://www.sqlservercentral.com/Forums/Topic1455052-2799-1.aspx
In short, try the restoring the database using TSQL code. I usually do. The WITH FILE clause is optional if there is only one backup set.
Can you read the file list of the backup?
-- Can you read the file list
RESTORE FILELISTONLY
FROM DISK = 'Z:\SQLServerBackups\AdventureWorks2012.bak'
WITH FILE=1;
GO
Check the validity of the backup.
-- Is this a valid backup?
RESTORE VERIFYONLY
FROM DISK = 'Z:\SQLServerBackups\AdventureWorks2012.bak'
WITH FILE=1;
GO
Try restoring the database.
-- Simple restore, source and target file names and location are the same
RESTORE DATABASE AdventureWorks2012
FROM DISK = 'Z:\SQLServerBackups\AdventureWorks2012.bak'
WITH FILE = 1
RECOVERY;
If you want to move the files to different names or locations, check out BOL.
http://msdn.microsoft.com/en-us/library/ms186858.aspx#restoring_full_db
In short, if it is a permission issue, you should see a error in the query window.