What computer operating system is being used for your Premiere Elements 14?
Does the Play button not working apply to all projects or just one particular one? If the Play button does not work, can use instead the computer space bar to start the Edit area monitor playback?
If all, then let us go through the usual drill of questions:
1. Is your video card/graphics card up to date according to the web site of the manufacturer of the card? Does your computer use more than one video card/graphics card?
2. Do you have the latest version of QuickTime installed on your computer with Premiere Elements, and are you running the program from a user account with administrative privileges?
3. Does the problem exist with and without the antivirus and firewalls disabled?
A consideration might be to delete the Adobe Premiere Elements Prefs file. I am not sure if we are ready for the uninstall/reinstall suggestion yet.
Please consider, and give more information so that we can answer with details customized to your situation. Please do not hesitate to ask if you need clarification on the questions being asked.