If your mac is 3 years old, then it likely has special storage on the machine containing the last version of the operating system that it used. It exists specifically for instances where you need to reinstall the OS, and it cannot be wiped. It replaces the old method where you had to have a CD or some other copy present. (I'm pretty sure it is stored independently of the HD, but I could be wrong.)
To reinstall the OS from the special storage inside your machine, boot to Recovery Mode:
- Turn on the mac
- While it is booting up, hold Command+R until the Apple logo shows up
- You will see a loading bar under the Apple logo
- Once the screen loads, you will see a window with four options
- Click the second one down – "Reinstall macOS"
- That will wipe the hard drive (whatever may exist on yours), installing a fresh version of whatever the latest OS was.
If that fails, you can install the OS from over the internet:
- Turn on the mac
- While it is booting up, hold Command+SHIFT+R until the Apple logo shows up
- You will see a spinning globe for a while
- Once the screen loads, you will see a window with four options
- Click the second one down – "Reinstall macOS"
- That will wipe the hard drive (whatever may exist on yours), installing whatever version of macOS your computer shipped with from the factory (it will be a 3 year old version) You need internet access for this to work.
Final Step:
Once any OS is installed, you can open the app store, and search for "Mojave OS" to download what is currently the latest macOS.
Like I said I don't think any of that requires a HD but please ignore me if I'm wrong. Good luck!