If you have circular logging disabled, you will be able to recover to the time of the crash. This is becausedisabling circular logging allows the transaction log files to accumulate until the databases are backed up. Once the backup has completed, all transaction log files except the five most recent (including the edb.log) will be deleted. As new messages come in, new log files are created. If the system crashes at 3:00 in the afternoon, and all the transaction log files since the last backup are intact, all you have to do is restore the databases (priv and pub) and restart the IS. This will cause the IS to read the uncommitted log files into the database, thus bringing the database up to date.
If you don't know if circular logging is disabled, open Exchange Admin and go to Organization|Site|Configuration|Servers|%servername% and open the properties of the server. Click on the 'Advanced' tab. Circular logging is right there. Both boxes should be UNchecked.
Good luck,
Bob