O que significa but with what was traveling through my veins at that moment, I needed to slip back to old faithful ?

See a translation

"[Considering how violent I felt], I needed to [go back] to using [my fists]."

If we are being poetic, instead of saying "I'm afraid," we might say "There's a chill in my veins."
Instead of "I'm angry," we might say "The blood was running hot in my veins."
Instead of "I feel violent," we might say "There's bloodlust in my veins."

In summary, if we are feeling a primal emotion like anger, we might say something appropriate about the contents of our veins. This is a weird English thing.

So, "with what was traveling through my veins" = "with the primal emotion in my veins"
From context we can assume that he is feeling violent/angry.
So, "with what was traveling through my veins" = "considering what was traveling through my veins" = "considering the violent feeling in my veins" = "considering how violent I felt"

So,
"[considering how violent I felt], I needed to slip back to old faithful."

"Old faithful" is a common saying. An "old faithful" is anything that the speaker trusts and has used for a long time. It makes the speaker sound more casual. From context (the speaker starts punching immediately after he says it) we can assume his "old faithful" is his fists.

So,
"[considering how violent I felt], I needed to slip back to [my fists]."

"Slip back" is just a fancy way of saying "go back" here.

So,
"[considering how violent I felt], I needed to [go back] to [my fists]."
=
"[considering how violent I felt], I needed to [go back] to using [my fists]."