I don't agree that China was isolated. Buddhism came in from India. The Silk Road brought trade from the West. There were invasions of Mongols. So I don't agree at all with the idea that China was isolated.
If you're talking about what makes a person Chinese it's at least mostly cultural, I'd say. Like you, I'm half Asian, but I grew up as an American and so my "Asianess" is only skin deep with the exception of things like a weakness for rice and soy sauce and such.
For people who are truly Chinese, what makes them that way is their culture. It is a set of attitudes that began with the idea that China was the "Middle Kingdom" and was therefore superior to all others. That was then overlaid with a helping of anger against the West because of things like the Opium Wars and the unequal treaties imposed on China. Nowadays, there's pride in China's deep history and its current success mixed with resentment of the West because of history and because of issues like Taiwan and Tibet.
To me, that's what makes a person truly Chinese -- yes, it's genetic, but I think that it's also largely cultural, beginning with the sorts of attitudes I've identified.
What do you think? Are you really Chinese? I'm never sure if I'm truly Asian or if I'm just a coconut -- brown on the outside and white on the inside.