If the distribution from your Coverdell ESA reported on Form 1099-Q was entirely used for Qualified Education Expenses, you don't need to enter it on your tax return (or on your parent's return). Just retain it for your records.
Here's more info on Form 1099-Q.
Unless you are required to file for other types of dependent income, you may not need to file a tax return. Click this link for more info on Dependent Filing Requirements.
As far as Schedule D info from your parent's return, there are many types of income reported on Schedule D besides dividends. Stock sales, other investment sales, home sales, land sales, business equipment sales, etc.
Here's more detailed info on Schedule D.
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