04-19-2017 10:45 AM
Welcome to HP Forums, this is a great place to get support, find answers and tips.
Thank you for posting your query, I'll be more than glad to help you.
I understand that your HP TouchSmart 310 Desktop PC powers on but the screen is black.
In order to isolate the issue, let me know the following details:
1. Do you get the HP Logo on the screen?
2. Do you get any beep sounds?
In the meantime, you may follow the steps under the sublink "Computer starts, but monitor is blank" in the link: Computer Does Not Start (Windows 7)
You have a good day ahead.