What's the exact, full, error message please?
Did you try the backup "manually" or using some "utility"? I'd be happier with a manual backup, in SQL, as that is most likely to give a clear message about the problem and will prevent anything else getting in the way and possibly giving a false error message.
BACKUP LOG MyDatabaseName
TO DISK = 'x:\MSSQL\BACKUP\MyDatabaseName_yymmdd_hhmm.BAK'
STATS = 10
-- , DESCRIPTION = 'Log backup yymmdd_hhmm'
-- , NAME = 'FooBar'
-- , COPY_ONLY
-- , NO_CHECKSUM
-- , CONTINUE_AFTER_ERROR
-- , NORECOVERY
-- , NO_TRUNCATE -- equivalent to COPY_ONLY, CONTINUE_AFTER_ERROR. Use if database is SUSPENDED
-- , NO_TRUNCATE, NORECOVERY -- for a best-effort log backup
If you get errors try commenting in some of the database corruption work-around commands.
Note that the log backup file created is required to maintain the CHAIN of backups, in the event of a restore, so the location where it is stored and its subsequent backup to Tape/whatever is important.
You might want to use COPY_ONLY or NO_TRUNCATE so that the normal Log Backup will include the log data in the normal way (once the problem is solved). However, that will not release log file space so if log file is growing, and disk space is an issue, then you probably do need to allow the log to be truncated.