There is no law preventing a 17 year old from applying to YC, nor do we have any rules prohibiting a 17 year old from applying to YC. But as the other commenter noted, the problem with minors is that they cannot enter into contracts that are not voidable at the option of the minor. In California, there is a lot of case law on this subject related to minors in the entertainment industry. If a minor is accepted into YC, then we would do our best to find a work-around.
In many places, a minor cannot enter into a binding contract nor own/control property of significant value. So that would leave me wary of entering into an agreement with a minor where I was to give them a lot of money and they might be able to arbirtrarily cancel our agreement, or their parent/guardian could seize control of assets unexpectedly.