Problem with 16x2 display

Actually, what I meant was plug the power into the normal plug and wire everything
up as you had originally but measure the voltage on Vin.
That will measure the powersupply voltage before the regulator circuitry.
I'm guessing you see 5v on Vin but something else on Vcc.

At below the dropout voltage, the voltage regulator will not work properly
properly so I wouldn't want to depend on it to supply power to anything including
the AVR.
To use the power input plug you need a higher input voltage.

As long as the power supply you have is a 5V regulated supply,
then you could make/buy an adapter to allow plugging it into the USB connector.
Power into the USB connector does not go through the voltage regulator.
On the plus side using the USB connector for power is more efficient since
the higher voltage doesn't have to be regulated down.
On the minus side if the wiring is backwards or the power supply supplies more
than about 6 volts, the 5v circuitry can be damaged.

--- bill