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Regarding this situation, please perform or check the following steps/information in order to troubleshoot this issue.
1. Compare the specs of your RAM with the supported RAM for your unit (DDR3L-1333/1600 1.35V SO-DIMM). It is very important that you are using compatible RAM module(s).
2. Test your RAM modules separately on each DIMM slot.
3. Are you able to access the BIOS? If not, please perform a BIOS recovery by following the instructions here: Intel® NUC Boards and Kits — BIOS Recovery Update Instructions
4. Here you can find the different Blink Codes and Beep Codes: Intel® NUC Boards and Kits — Blink Codes and Beep Codes
5. Also check that all the connections are properly set. (HDMI, power adapter, RAM, SSD, etc.
6. Test the system without any additional components, if it works, add one component at a time in order to check if one of them is the problem.
7. Test a different power adapter if doable
About the adapter, the recommended setting would be a straight connection (Mini DisplayPort to Display port) we cannot assure that adapters would work. You could test your NUC with a different display (monitor, TV) in which you can use a straight connection.