Did your operating system back the developer key up? In Windows file backup, it may have backed it up to a separate drive if you've enabled it. I'm sure Mac has similar.
What exactly is the nature of the system failure? OS won't boot? System drive failed?
If your system drive failed, it may still be possible to recover some of the existing contents. (Unfortunately this is more likely if you have an old spinning HDD as opposed to a modern SSD. Spinning HDDs usually fail gradually, while SSDs often fail catastrophically.)
For example, if you have another computer, you can connect the drive to to that computer using a USB to SATA converter, and try to access the contents that way. (Either using the standard file explorer or a speciaiized recovery tool).
If that isn't practical/possible, you could always take your computer (or just the drive) to a computer repair shop (yeah, I know these are few and far between these days).
It's too late, but I do agree that you should have multiple copies of your developer key. It's such a small file and there's basically zero cost to keeping extra copies of it around. (I upload encrypted copies to various cloud providers.)
The developer key is a security measure that prevents developers from making updates to apps that do not belong to them. We do not retain your key—your local copy, and any backups you may make, are all that exist. If a developer key is completely lost, the only option is to re-publish your apps to the store using a new developer key, and direct your existing users to the new app listings for the latest version updates.
