Hi Lawrence. What OS are you using? And did you purchase from Adobe or somewhere else?
Did you watch the installation process? Did it appear to complete the installation? Did you get any errror message? Have you rebooted your computer?
Did you disable your anti-virus and firewall software while installing?
If you are on Windows, go to C:\Program Files\Adobe\Photoshop Elements 2023. Does the program open if you double-click on the file named PhotoshopElementsEditor.exe. (Don't be fooled by the blue icon for the folder. And pay close attention to the name of the file I have given you.) If that doesn't work, right-click on the file and choose Run as Administrator from the context menu.
If you are still having trouble with the installation, try contacting Elements support. You can start a chat session by clicking on the blue Contact Us button under the Help & Support menu at Adobe.com.