Corrupted mdf file causing the backup job to fail
Given that you can connect to the database you may actually be in pretty good shape.  There are a number of methods you can use that might work but here is one.


Create a new database preferably on another disk because the possibility is that your disk is corrupt.
Use generate scripts to generate a script for your existing database.  Include all database objects and permissions.





Run the script on your new database to create all of the structures you need.
Either manually or through a tool (Import/Export Wizard for example) copy the data from each of the tables on your corrupt database into the new database.  Unfortunately this is the step most likely to have problems.  If you do have a problem it will hopefully be with only a few records and you can use the Import/Export Wizard to generate an SSIS package and change your error setting for that particular table to ignore failures.


Either way once you are done take a backup.  (Of course)