Q:

Arduino Uno Issue: No output power

I am currently a first time Arduino user. I decided to get one and start prototyping basic types of circuits.
I have built various basic circuits with the Arduino Uno prototype board and it worked completely fine. I am using the Arduino board to source power to my circuit (5V). However, after building the following circuit, everything stopped working:

simulate this circuit – Schematic created using CircuitLab
I don't get output from any of the Arduino pins and I cannot upload programs to the board. The yellow LED still blinks, and the green power LED remains green and active.
I cannot figure out how I managed to burn the board. The current is around 22.72mA, which is pretty far of the 40mA absolute rating.

A:

You need to have a current limiting resistor for each of the LED segments. Sharing one resistor between them all is a very bad idea, as multiple lit LEDs (in parallel) will be using the same resistor - see this excellent answer to Why exactly can't a single resistor be used for many parallel LEDs?:

The main reason is because you can't safely connect diodes in
  parallel.
So when we use one resistor, we have a current limit for the whole
  diode section. After that it's up to each diode to control the current
  that goes through it.
The problem is that real world diodes don't have same characteristics
  and therefore there's a danger that one diode will start conducting
  while others won't.

I would hazard a guess that you've drawn too much current, or, in your case, tried to sink too much through the PWM pin.
Also, it would (probably) be better to use individual data pins, not PWM pins, to turn on each segment, rather than connecting all of the segments to just one pin. It just seems a bit odd to do it that way.

