I’ve had a HP PhotoSmart S20 scanner for years and never really got around to seriously scanning in my slides & negatives. Now that I have the time and interest, I find it will not work with Windows 10. Fortunately, I have a Windows 7 laptop that seems to handshake with my scanner. I follow these directions found by googling “HP Photosmart S20 Windows 10” on the Dell Forums. Some advice is to install Vuescan which is supposed to install a compatible Win 10 driver but this isn’t true. In fact, on Vuescan’s website, it says to make the scanner work requires a HP driver.
After installing ps804en,exe on my Windows 7 laptop, the scanner appears under ‘Devices’. I’ll see if and how it works before spending a lot of time trying to get it working on my desktop running Windows 10.
If you are trying to get your scanner working on newer versions of Windows. Give the following instructions a try. I’ll add the driver download link from a good resource that worked for me.
https://www.helpjet.net/Fs-60847854-80177087-39633014-devices.html

If you have HP drivers installed, follow the first 12 instructions. Otherwise, start at Go to www.HP.com or get the driver from the helpjet link above, or google ‘ps804en.exe’. You’ll get several links including cnet.com.

• Disconnect the scanner from the system
• Click Start- (Settings)- Control Panel
• Look to the left. If listed, click “Switch to Classic View”
• Double-click the Add or Remove Programs icon
• Look to the left. If listed, click the Change or Remove Programs button. A listing of all installed programs should be available
• Select all HP scanner applications/drivers you want removed and then click the Change/Remove button
• The InstallShield Wizard dialog box, select the Remove check box
• Click Next
• If you get a window for “Remove Share Component”, click “Yes to All”
• If you get a window for “Remove Share File”, click “Yes to All”
• Click Yes
• When finished, close all boxes
• Go to www.HP.com
• Select ‘Home & Home Office.’
• Type ‘S20 ps804en.exe’ into the top Search field [press the ENTER key]
• Click HP Photosmart s20 photo scanner
• Select ‘Download drivers & software’ from this screen.
• Select ‘Microsoft Windows XP.’
• Select ‘PhotoSmart Scanner (SCSI) and S20/S20xi Photo Scanner (USB) Software.’
• Click ‘Download now’ to being downloading ps804en.exe
• Click Save
• Click Desktop
• Click Save
• When done, double-click the downloaded file
• A Windows-based message will appear during installation that recommends stopping installation because the HP Photosmart software has not passed Windows Logo testing
• Ignore this and click ‘Continue Anyway’
• Follow the prompts to finish loading the software
• Click Start- Shutdown- Restart- OK or Click Start- Turn Off Computer- Restart
• Reconnect the powered on scanner

Helpjet’s driver page also has instructions you can try:

Here is a step by step manual guide for HP PhotoSmart C5101A – S20 software installation process on Windows 7 / 8 / 8.1 / 10 / Vista / XP.
1 Download ps804en.exe file for Windows 7 / 8 / 8.1 / 10 / Vista / XP, save and unpack it if needed.
2 Switch on your new hpphotosmartscanner hardware.
3 Right click on the My computer icon and push Properties tab then. Choose Hardware tab. Click on Device Manager button.
4 Find your HP PhotoSmart C5101A – S20 device in the list and press double click on the hpphotosmartscanner device. Click Reinstall driver button.
5 Choose Install from the specific location and click on the Browse button. Click on the Next and Finish button after that to complete the installation process.
6 After these steps, you should see HP PhotoSmart C5101A – S20 device in Windows peripheral manager.