Standalone Arduino Serial debug not working

The Next Question is in regard to the NECESSARY bypassing... .1uF caps are cheap... Is your time so valueless that five cents is more valuable?..
ALL OF THE PARTS ON ANY ARDUINO BOARD ARE THE ABSOLUTE MINIMUM REQUIRED TO CAUSE THE CIRCUIT/CONTROLLER TO WORK AS IT SHOULD. NONE Should ever be left out...
To do so is to indicate that you know more than the designer did... So that being the case where is the issue?.
While this might not apply directly to your case it is applicable to many others and perhaps food for thought for you..
The other very common issue IS batteries. The Minimum recommended is 3 AA cells applied to Vcc (Not 4). This will provide 4.25V to the controller and is a good beginning If you can't use the USB connection for power.
Best in my Direct experience is a SMPS 7.5V "Wall Wart" as it will allow the linear regulator to work better within it's specifications.
Consider that a 9V external PSU is 9/7.5 or 20% more power Wasted as heat in the regulator and a 12V external PSU is 12/7.5 or 60% more Wasted Power in the linear regulator. Food for thought?

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