You cannot use Internet Recovery on your model but you can use the Recovery HD if it's functioning.
Reinstall El Capitan or Later Without Erasing Drive
Please be sure you back up, if possible.
- Restart the computer. Immediately, at or before the chime, hold down the Command and R keys until the Apple logo and progress bar appear. Wait until the Utility Menu appears.
- Select Disk Utility and click on the Continue button.
- Select the indented (usually, Macintosh HD) volume entry from the side list.
- Click on the First Aid button in Disk Utility's toolbar. Wait until the Done button activates, then click on it.
- Quit Disk Utility and return to the Utility Menu.
- Select Install OS X and click on the Continue button.
This reinstalls macOS over an existing system.
Install El Capitan or Later from Scratch
If possible, back up your files.
- Restart the computer. Immediately, at or before the chime, hold down the Command and R keys until the Apple logo and progress bar appear. Wait until the Utility Menu appears.
- Select Disk Utility from the Utility Menu and click on the Continue button.
- When Disk Utility loads select the target drive (out-dented entry w/type and size info) from the Device list.
- Click on the Erase button in Disk Utility's toolbar. A panel will drop down.
- Set the partition scheme to GUID.
- Set the Format type to APFS (SSDs only) or Mac OS Extended (Journaled.)
- Click on the Apply button, then wait for the Done button to activate and click on it.
- Quit Disk Utility and return to the Utility Menu.
- Select Install OS X and click on the Continue button.
This erases the disk, then installs a fresh copy of macOS.
If you cannot perform either of these, then you may need to wipe the drive and start from Snow Leopard 10.6.8. If you don't have Snow Leopard, then you will need to find a copy on eBay or Amazon. Apple is no longer selling Snow Leopard DVDs.