I have an HP Laserjet 1536dnf MFP and the printer cable is unrecognised by my tower or my new laptop

[Herbacide]

Both my old printer cable and a brand new one gets a USB Cable not recognised  when I plug it in and of course I can't print or scan. This happens on my old tower running Windows 10 and my new laptop running windows 10.

[sandytechy20]

@Herbacide

Welcome to HP support community.

1. Turn off the printer and your computer, and then disconnect the USB cable from the computer.

2. Inspect the cable.

   • Look for any damage. If the cable is damaged, replace the cable.

   • Check the length of the cable. If the cable is more than 3 m (9 ft 10 in) in length, replace the cable with one that is shorter.

3. Connect the cable to a different USB port on the computer. The port should be USB 2.0 or greater. If you use a USB hub or docking station, connect the cable directly to the computer.

4. Make sure the cable is fully secured to both ports.

5. Turn on the computer, and then wait for the computer to complete the startup.

6. Turn on the printer.

Run the HP Print and Scan Doctor

 Download and run the HP Print and Scan Doctor to automatically diagnose and resolve printer hardware and connection issues.

If your printer is not found on the Choose Your Product step, click My product is not listed for steps to connect the printer.

Perform root level uninstalltion to remove all the printer related software's.

• In Windows, search for and open Programs and Features.
• Select your HP printer.
• Select Uninstall.
• In Windows, search for and open Devices and Printers.
• In the Devices and Printers window look for your HP Printer. If you see it listed, right-click on it and choose "Delete" or "Remove Device.”
• Open up the run command with the "Windows Key + R" key combo.
• Type printui.exe /s and click OK.
• Click on Drivers tab.
• Look for HP Printer driver. If you see it click on it and click Remove at the bottom.
• Select OK.
• Remove all instances of the same.
• Select Apply and OK on the Print Server Properties windows.
• Close Devices and Printers. 
• Restart the PC again.

Download and install printer full feature driver 

Click here to download the driver.

Let me know if that helps.

To thank me for my efforts to help you, please mark my post as an accepted solution so that it benefits several others.

Cheers.