MS SQL Server 2008 Transaction log file back up failure
Have you tried running a full backup followed by another transaction log backup?  What error messages are you getting?  


  We know the logs backup fails, but if it's in simple recovery mode and
  the database is backed up but the log back up fails would I be able to
  recover the database? By recover lets get this straight, I'm talking
  about getting the thing working again by simple restoring from my last
  back up?


If the database fails, you can recover the database with the last full backup regardless of whether it's set to full or simple recovery.  Simple recovery doesn't support log backups at all.  So basically, you'd lose everything from your last full backup forward.  


  So wouldn't creating new log file and removing the old log file (but
  leaving the old file on the disk) be the thing to do?


NO.  DO NOT DELETE YOUR LOG FILE.  You'll probably kill your database and the symptom you're trying to fix is that it won't back up properly.  

I'm going to recommend this article, "A beginner’s guide to SQL Server transaction logs."  Especially this bit:


  Can SQL Server database work without a transaction log?
  
  No, that is not possible due to the SQL Server design and ACID
  compliance. ACID stands for atomicity, consistency, isolation, and
  durability.


Also this article on Full vs. Simple recovery.

To crib from this article:


Run dbcc checkdb on the database
Stop all user activity in the database
Switch to the SIMPLE recovery model (breaking the log backup chain and removing the requirement that the damaged portion of log must be backed up) (which you've done, yes)
Switch to the FULL recovery model
Take a full database backup (thus starting a new log backup chain)
Start taking log backups