You have not mentioned the source of your "unearned" income. The refundable child-related credits are based on having income from working. If you claim a dependent over the age of 16, you get the non-refundable $500 credit for other dependents---which can reduce the tax you owe but is not given to you as a refund. If your income does not come from working, you are not eligible for the child and dependent care credit, which is for working parents who must pay for someone to care for their child while they work. Similarly, the earned income credit is based on income from working--so unless you work, you cannot get EIC.
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