So I went through all of the tutorials, and I have managed to successfully make a department store profitable, but one thing isn't clear to me. If I start a new game and instead of first going into retail try and go farther up the chain, like starting with a farm or a factory, I notice that for some reason there's never any sales. I have a sales unit, and I even have an advertising unit linked to a nearby media outlet, yet no one seems to want to carry my stuff. What am I doing wrong, if anything?

Sounds like you are going into manufacture business and not engage into the retail business. If it is the case, it is normal that no sales in the beginning, and you do not need a marketing department.
I played the first scenario with this strategy, (so far the only scenario I have cleared after 5~6 failure) after about half a year, your product will eventually get sold to other company. It just like an OEM / ODM business, other company buy your product and sell to the customer. Therefore you do not need to create a brand name for the "consumer market", thus marketing unit is useless. Because your target is "non consumer market", product price and quality is the big concern for your "customer".
Same thing goes for the raw material. If you produce raw material, other company buy it and use it on their own production line.

Yeah, when you're selling non-retail stuff, you're not selling it to a simulated market, like with retail goods. You're selling it to other, computer controlled companies. In the beginning, the world will be "empty", i.e. you need to wait for the computer players to set up their stores and factories et.c. before you can expect them to buy anything from you. That can take some time, depending on what they're up to, what style of company they are, what you're selling, et.c.

Honestly, trying to make a living selling stuff to the computer players is a bad idea. It can be a good way to make some extra money, provided the computer players aren't just cannibalizing your own sales, but in the end I think you'll find that the "internal sale"-button is your best friend. :-)