SQL Server transaction log file refuses to grow
To fix the issue in the short term manually grow the log file since that's best practice anyway.  

If the log file will end up being multiple GB grow it in 1 - 4 GB increments to get there.  

If you don't know how big it's going to get I would recommend using at least 1 GB increments.  This is a blocking operation so it should be done during a low use time if at all possible.

To discover why your problem is happening check for errors in the SQL error log, not just error message from the failed statement.  There may be an error stating why it couldn't grow.  

You can also look at activity monitor to see what the sessions that are having problems are waiting on.  Right click on the instance in SQL Server Management Studio (SSMS) and click on "Activity Monitor."  Once you have it open look at the blocking chain (Blocked By and Head Blocker) and the Wait Type to see what is causing the issue.

To determine why the DB is getting created with a MAXSIZE of 70 run Profiler to catch the CREATE DATABASE statement.  That will tell you what query is getting run so you know if SQL is getting the correct query or not.