Change database file path with SQL not running
Do not restart sql server service or try to offline the db

What you can do is ADD a secondary log file using 

ALTER DATABASE [dbname] ADD LOG FILE ( NAME = N'dbname_log2', FILENAME = N'M:\dbname_log2.ldf' , SIZE = 20480KB , FILEGROWTH = 1024KB )

Check log file usage :

DBCC SQLPERF(LOGSPACE); 


This way the db can be online and you can start taking log backups (or if point in time restore is not required, then change to simple recovery) to truncate the log file.