Hello Greetz,
Thanks for asking and I am really sorry for the trouble you are facing with website getting crashed.
If the backup is broken then it would be a bit difficult for you to rebuild the website again using the same backup file. However, if you made changes in the theme files and if you are able to extract the files then you can take out the theme files under /wp-content/themes/x/ or /wp-content/themes/x-child/ folder. Can you let me know how did you took backup of the WordPress installation? Did you used any plugin for the same? If you could let me know the plugin name, may be I can tell you the path of sql file that you can use to import on the server and some work can be saved.
Next, try and look for the media files under /wp-content/uploads/ folder. I also suggest you to get in touch with hosting provider, some hosting companies do keep backup file on there system. Maybe you can give it a shot and enquire about backup.
To have a grid layout, I suggest you to take a look at Essential Grid plugin that can be installed from X > Validation > Extension. To get started with Essential Grid, please take a look at following article.
Thanks.