Depending on the severity of the system error, you might be able to backup the current transaction log using the NO_TRUNCATE option.
Thereafter, restore the database on another system following the steps you described, and if you were able to backup the current log, use the STOPAT option with the RESTORE LOG syntax e.g.
RESTORE LOG MyDB FROM DISK = 'e:\backup\logbk.bak' WITH STOPAT = 'Jul 27, 2004 1:59 PM'
SQL BAK Explorer - read SQL Server backup file details without SQL Server.
Supports backup files created with SQL Server 2005 up to SQL Server 2017.