There had been a lot of issues with a VGA to HDMI adapter specially if it's not design for a laptop or PC and is just for projectors. But please do try these troubleshooting steps that may help in solving the issue.
- First is to press the Windows key + P at the same time and select between Extended or Duplicate display then press Enter.
- If these doesn't work try to uninstall/reinstall the graphics card driver.
- Open Device Manager and uninstall the graphics driver.
- Next is to check Programs and Features as well and uninstall anything related to your graphics card.
- Once done, download and install the latest driver from the manufacturers site.
- Reboot your laptop once the latest driver has been installed.
- Test if your laptop will connect to your TV again after the reboot. (press Windows + P again then select)