"Parking" a domain doesn't mean you're making whoopie in the back seat - it means the wheels on the car aren't turning.
Most places, a parked domain doesn't do anything at all. At Dreamhost, they stretch it a bit by giving you a mail server on the domain. Silly geese!
So if you are wondering why www.myparkeddomain.com isn't displaying pages, that's why.
If you are wondering why www.mydomain.com isn't displaying pages, it is not because you have www.myparkeddomain.com as well. It would be something else.
In the control panel, click on "manage" (under "domains") and your domains will show up on the right side. Under the domain you are concerned about, there will be a line that says web. Click on "edit" at the far right of this line.
The page that appears will show "Web Directory:" under "a fully hosted domain". That's the directory where you would put your "index.html" home page. If "a fully hosted domain" is selected, and your files are in that directory, they should appear.
Yeah, parked domains are free, and fully hosted domains cost. Seems unreasonable to me, too, that Dreamhost wants to be paid. You'd think that happy dreamhost employees would be overjoyed to work for free, but apparently they are greedy and want paychecks.