How is unrelenting trauma pain possibly connected to mood?

Variable. Any form of chronic pain can effect mood and vice versa. It's become clear that chronic pain can lead to depression, anxiety etc. And treatments for depression can decrease pain. Ex. Cymbalta, (duloxetine) an "anti-depressant" medication has been shown to improve diabetic nerve pain. Optimal treatment of chronic pain often involves pain medications (of various types) and treatment of associated depression.
Mindful of Mood. Chronic pain actually results in neurotransmitter changes in several areas of the brain, specifically the limbic system and forebrain. These areas are directly related to mood and behavior. Since the chronic pain experienced by the individual changes brain chemistry over time it is inevitable that mood will become affected. This is why effective pain management must address behavioral changes.