We start things off with his being equipped with a bog-standard Liography father. You know the kind: a sullen dullard too in love with a vice that makes everyone else's life worse (in his case, Demon Rum) to care about the negative effect it has on those around him. When Ol'No Name Given was sober, he was a loving, hard-working father but like Mrs Dingle's asshole husband, he couldn't stop slamming down the booze and waling on the wife he slowly drove to drink.
This leads to his unseen but actually named mother Corina who was a seamstress for a dry-cleaner or something. As I said, dealing with his binge drinking did a number on her self-worth and led to her own downward spiral. It also lead to Gordon's much older (and never actually hinted at or referenced) sister Ardith taking off as soon as she possibly could. It's also why he's into cars, our Gordon; cars are a means of escape from "Hey, Stupid, Ever Hear of AA" Town.