Hi there Neilgr85!
There are a couple of articles here that I would like to point out in an attempt to resolve your issue. First, to answer your question directly, you can pull information off of the computer by putting the computer into Target Disk mode and using the Thunderbolt port to transfer to a fully functional computer. An article about going that can be found here:
If your MacBook Air is having trouble starting up, then I have some articles that may be able to help you resolve that issue as well. First, this article about what to do if you can't turn on the computer:
If your computer turns on, but is unable to get to the login screen, then you will want to reference this article:
Thanks for being a part of the Apple Support Communities!