No digital pin output (pins 10-13)

I have an UNO rev. 3 that I can't get these digital pins to go to a "high" level. I'm using Windows 10 pro 1709 and version 1.8.5 of the IDE. I created a simple sketch to test if it was my code (in the original program) or something else (see below). This is a new Arduino. I have also done the loop back test (it passed) and I have uninstalled and reinstalled the IDE, sketch, and USB driver. I'm really frustrated at this point. Any help would really be appreciated.

Here's the code:
void setup() {
pinMode(10, OUTPUT);

void loop() {
digitalWrite(10, HIGH);

I checked the continuity of the wires and the connections on the Arduino and they were good. A thought crossed my mind that perhaps the relay board I was using needed to be grounded to the Arduino in order to work. It turns out that was the issue (the relay board is a 5V 4 relay module available from RobotShop.)

Moderator, if you could mark this issue as solved and move it to the correct address that would be appreciated.

How are you determining that pin 10 is not HIGH?