Not, I'll not, carrion comfort, Despair, not feast on thee; (1)
What's for dinner? Why, it's a nice big plate of Despair. That may sound unappetizing (and the speaker does reject this meal as gross, yucky "carrion"), but people dig into this dish on a regular basis. We've all been there, not wanting to be cheered up or told by some smiley someone that "it'll get better." In that way, despair and depression can be dangerously attractive mindsets that seem like "comfort" when we just want to wallow in our own sadness.
Not untwist—slack they may be—these last strands of man In me ór, most weary, cry I can no more. (2-3)
Sure, the speaker is rejecting these sad feelings, but that's only after he's experienced them in the first place. At one point, he felt as though his very being ("strands of man") was coming undone. That's enough to make anyone weary and want to give up.
But ah, but O thou terrible, why wouldst thou rude on me Thy wring-world right foot rock? lay a lionlimb against me? scan With darksome devouring eyes my bruisèd bones? and fan, O in turns of tempest, me heaped there; me frantic to avoid thee and flee? (5-8)
Imagine being pinned under the paw of a giant, ferocious lion that's looking down at you like you are a tasty snack. That's a pretty helpless, terrifying feeling—one that our speaker has just experienced. His despair went way past your typical brush with sadness. He was both desperate and lucky to get out of the experience.
[…] That night, that year Of now done darkness I wretch lay wrestling with (my God!) my God. (13-14)
By and large, a "wretch" is not a happy person. It turns out that the speaker was in this sad state for a full year, which seems impossibly sad. Even if he had suffered for a night, he acknowledges, he underwent a severe test. Wrestling with God, after all, is not for the faint of heart.