Not even a slim chance. There's more of a chance of being eaten by a shark (which isn't even a slim chance). I have handled many garter snakes and none of them have ever bitten me, much less put a rear fang in me. At any rate, the venom, as I understand it, is weaker than a bee sting (which I incur from time-to-time since I keep bees). Hognose snakes are likewise endowed with rear fangs for the toads they eat. I have never even seen one of them bite or strike. You would have to be feeding it and holding the prey they eat to accidently get bitten. Who does that?The size and the dull brownish color with diamonds sounds like a gray rat snake (aka chicken snake). The green stripe, I don't know. I don't believe garter snakes have diamonds but they do have green and even blue stripes.
Garter Snakes are actually venomous. However their fangs are very small and located at the back of their mouth. They grab a toad and chew on it in order to inject the venom. They are nothing to play with. There is probably a slim chance of being bit with the fangs, but still a chance.
I agree most likely a rat snake as they are common and often eat eggs.