How can I market a low-budget video production business?

The trivial answer to me would be 

 

1) Create some stunning show casevideos 

2) Upload them to a professional looking YouTube Channel

3) Market your show case videos and your business as much as you can

You can engage local and/or start-up organizations.
For example, you can offer a newly-opened restaurant to produce a20-30 seconds ad for as low as $1,000-1,200 (depending on the manpower while keeping in mind to maintain the footage to an efficient minimum) wherein you display the atmosphere of the restaurant & the quality of the food.
This is just an example.