If you're talking about a RAID array write cache backup battery, then you either must replace it or must disable the write cache or you are risking a corrupt database.

Start with this

http://www.simple-talk.com/books/sql-books/troubleshooting-sql-server-a-guide-for-the-accidental-dba/

As for backup strategies, don't start with the backups, start with the business requirements for maximum data loss. If the business thinks that there will be no more than 15 minutes of data lost in any disaster (and losing a few hours would be catastrophic), then a strategy of weekly fulls and daily diffs could result in unpleasant surprises and job losses (probably yours)