There are a number of ways a small business such as yours can advertise without spending money on a big ad campaign. I would first determine who your target markets are. You have a very specialized business, so a big ad campaign would be a waste of money anyway. In other words, you would be spending money to reach people who don't really need your services. Really think about groups of people who would need your services, and focus on those.
You may have tried some of these things, but here are a few ideas.
To begin, I have a small marketing company. People with companies such as mine are often in need of people with your skills. Contact small ad/marketing firms in your area and let them know of your services. They may very well job work out to you.
If you design logos, the people in need of those are your start up businesses. Do you have a business incubator or a SCORE office in your area? If so, pass your contact information on to them. The Chamber of Commerce might also be a way to reach new businesses. Although many of the companies you find there would already be established, some may be in need of a new logo.
Send a basic news release out to your local paper or business magazine announcing the launch of your business.This doesn't target a specific group, but it's free if you can get a mention in the paper.
The type of business you are in really does lend itself to the Internet. Make sure you have a basic online portfolio of your work. Then, with all information you distribute, make sure you have a link to that site so people can see your work. Logo design and illustration can be done from your location for anyone in the world. As far as the illustration part, there may be people looking for someone to illustrate their e-book. Do a search for freelance sites. An example is www.ifreelance.com. They do charge a monthly fee, but it's fairly low. You create a profile and bid on illustration jobs submitted by individuals and companies.
With the kind of work you do, you're really restricting yourself if you only focus on local work. To get your business going, focus on both local and online business.
For more ideas for marketing small business, visit http://www.marketing-small-business.net