If he's getting ready to shed, he's not going to be hungry. Wait until after the shed cycle, then offer food.

When a snake is getting ready to shed, the eyes turn a milky-blue color. This is a fluid the snake secretes to loosen the top layer of skin. They will turn clear, and then a couple of days later, he will shed. Make sure there's enough water in the enclosure to immerse himself in.

It's not uncommon for garters to refuse to eat when they come into a new environment. If you just got him, give him some time, and don't worry about whether he eats or not. Now, if he sheds, and then after a couple of weeks, he still hasn't eaten, then it's time to worry.

If' he's a baby, a pinky might be a bit big for him. Rule of thumb: try to feed nothing larger than the snake's head, even though they are capable of eating things much larger. Also, try chopping up nightcrawlers into pieces; baby snakes love nightcrawlers.

I don't know about chicken broth. Chicken isn't one of the snake's natural prey. Try scenting the pinky with fish, nightcrawlers, or frogs.

Also, how big is your snake? Can you post pictures of him?