As it happens I have been looking for an entry level software engineering position in Ohio recently as well. Although I have been working in industry for a year, I am still looking at only entry level jobs. Here are some things Ive noticied about the market that influence how hard it is:
1 Skill set. Ohio is a Microsoft state. If you have primarily Java or C++ skills, you may find it harder to find a job than you would with .NET. There are still jobs, and you will still find one, but it may take longer.
2 Not all cities in Ohio are equal. Columbus and Cleveland are unquestionably the centers for software engineering in Ohio, with Cincinnati having fewer opportunities and Toledo being a poor option.
3 Many companies in Ohio are looking for cheap programmers, not software developers. If you just want money and experience, you may consider searching for these easier to find jobs.
As for the lack of response, this is just how job searching works. You can safely expect that even if you have an amazing resume, you will be ignored by 90% of recruiters. They get hundreds of resumes and dismiss the majority more or less at random. For this reason its good to deal with people you can email directly at the company rather than just Indeed.com etc. Another good option is to listen to third party recruiters who will do the same on your behalf. You may also want to see if the school you graduated from has any sort of job finding tools available to you, or perhaps if your school has a special relationship with any particular companies. For example Bowling Green State University sends a disproportionate number of graduates to Progressive in Cleveland, and HMBNet in Columbus. Shoot your former professors an email asking if they have any suggestions.