Base on your description, I recommend you doing the following steps:
- Disconnect all components from the NUC and Press and hold the power button with no other devices connected to the system for about 20 seconds.
- If you have more than one SODIM stick test just one stick in the system.
- Test a different memory stick if possible (brand and Model).
- Test a direct connection between your monitor and your NUC.
If after doing this steps and testing different hardware the issue persists, I would recommend you contacting your local support so they can help you with a possible replacement.
My local support would be what? I am upstate New York. Shouldn't this be covered under warranty since I have only had the device for less than two weeks.