Hi Keith,
The root cause of error “The transaction log for database 'ASPState' is full” is you didn’t backup or truncate log. SQL Server doesn’t automatically truncate log for the purpose of restoring database when it is damaged. Hence, with using that database, the .ldf file becomes larger and larger until fill with the hard disk.
To resolve this issue, you should backup and truncate log every some time. The simplest way is creating a job in SQL Server to backup log and set this job to run every some time (for example: every two weeks).
Since the .ldf file has grown to 2 GB, I recommend you first shrink the ldf file. To do so, please refer to the following link:
INF: Shrinking the Transaction Log in SQL Server 2000 with DBCC SHRINKFILE
http://support.microsoft.com/kb/272318
By the way, set the Recovery Model from full to Simple can decrease the .ldf file growth speed. Just for your reference, here are some helpful articles. You can read them if you interest in.
Selecting a Recovery Model
http://msdn2.microsoft.com/en-us/library/aa173531(SQL.80).aspx
How to stop the transaction log of a SQL Server database from growing unexpectedly
http://support.microsoft.com/kb/873235
INF: Causes of SQL Transaction Log Filling Up
http://support.microsoft.com/kb/110139