Hello,
If you are simply trying to distinguish new tickets from others. I have two different ideas for that:
You could use the custom fields for tickets. Set the default value of the custom field to 'New Ticket' and make sure the custom field can only be seen by agents. Then when the agent replies, have them change the custom field. Then you can have the custom field show in the grid and sort by that.
or
you could change the group of the tickets that have been replied to. Have a Incoming tickets group and a 'replied to' group then make an event for message sent with an action to transfer the ticket. Then you would just need to sort by group.
Hope this helps,