Arduino Uno - External Power not working properly
The only difference between powering from USB and powering through the barrel jack is the voltage is reduced to 5V through a Low Dropout (LDO) voltage regulator. These are typically a clone of the popular LM1113-50 and vary in current handling capacity from around 500mA up to 1A.

I notice your board is not a genuine Arduino - therefore the components used may be at the cheaper end. So we'll assume a low-grade LDO that only handles 500mA before going into thermal shutdown with good heatsinking. Since there isn't on these boards we shall therefore assume a maximum of 400mA before it gets too hot. Probably somewhat conservative.

So if your entire circuit is drawing more than about 400mA you can expect the regulator to shut down, or at least to reduce the current and/or voltage available.

The fact you're seeing 4.8V rather than 5V could be an indication that there is voltage droop occurring - i.e., the regulator is not able to supply enough current so the voltage drops. This would be accompanied by the regulator getting very hot.

The regulator is the device with 3 pins on the right side and a single tab on the left directly above the barrel jack socket. See how hot that is getting.

As a rule of thumb if you can hold your finger on it without crying for 10 seconds it's not too hot.



Another thing you can do is to reduce your circuit to the bare minimum. Unplug absolutely everything and upload the Blink example sketch. Power that from the external DC and see if the LED blinks for you. If it does then the power supply is working OK. You can then add your peripherals one at a time to see when it fails.

If it doesn't blink then there must be something inherently wrong with the supply.

One possibility is that the LDO is oscillating due to insufficient or incorrect input and output capacitors. This basically means the "5V" voltage it gives out is actually wildly swinging between say 4.5V and 5V or 4.75V and 5.25V, which really confuses the microcontroller. Cheap LDOs are often more sensitive to the capacitors they are paired with and can suffer from this kind of problem.

To diagnose that kind of thing you would really need access to an oscilloscope to analyse the voltage. 

If it is oscillating a 10µF ceramic capacitor connected between the lower two pins of the LDO (as orientated in your picture - that is Vout and GND) may cure it. A 1206 surface mount capacitor fits nicely across those pins and is reasonably easy to hand solder. You could also try a through-hole capacitor (ceramic again) between 5V and GND on the power header, but you really want it as close to the LDO as you can get it, so soldered direct to the LDO's pins is best.