If I remember correctly the licensing terms are, that once the license is expired, we will no longer be able to get updates, but the software will work.
Our license has expired, and we don't have an extension yet (simple oversight, person in charge of that got sick). How do I start up in this condition? When I select the current license, It simply doesn't accept this file.
The licence you have should be "perpetual" so it should continue to work without any expiry date. In some situations an expiry date is set in a licence while for example a security device is switched to another one, but generally licences should last for as long as you are using the same major version of the application.
I suggest you contact your normal support channel for assistance with this issue as it is difficult to discuss details of your particular licence here in the forum.