Personally, I believe the issues as to why my professor doesn't "know" how is because we're conducting this research at a community college level. She said to me she "didn't know how" because she's "a marine biologist by training." It may just be that's an excuse.
Community college faculty are not always PhD professionals, though they often are. Therefore, it's possible that your professor genuinely doesn't know how to get published. It sounds like she has more background in the actual scientific field (practice) than academia, which is great for teaching but not as helpful for research/publication.
Personally, I don't feel that the research is scientific enough for hard science fields like Neurology. I feel that a hard science would say we have left too many variables unaccounted for (e.g. we recruit from the Physical Education dept and don't account for what classes or other exercises the subjects do). However, when I was in undergraduate doing psychology, I saw all kinds of flimsy things like this being published, so I'm thinking something might take this.
All I can say to this part is... WOW. If you, as a community college student know that your research is not scientific enough for hard science fields, then I'm not sure what the motivation is to publish. I'm aware of the tendency for pre-meds to do things just to "check off" items on the list of perceived "must haves" for applying to medical school. But, it's not easy to get published in a reputable journal and getting published in a less-than-reputable journal is probably not going to accomplish what you hope. It's kind of like saying you were published on someone's blog. Not really very impressive and certainly raises suspicions of doing things for the (desperate) sake of appearance rather than actually being a researcher and going through the typical process. Usually, the motivation for publication is to advance the knowledge base in a certain field. Does your research significantly contribute to the understanding of some aspect of a specific field? If not, I'm not sure why it should be published.
Regarding the "flimsy things" you saw being published as an undergraduate, I want to express my observation that psychology research is actually very difficult to do well and equally difficult to get published. In my experience, it involves some of the most complex statistical analyses and careful, almost obsessive, research design. I have not seen much that is "flimsy" being published in a reputable psychology journal these days. Are you sure that what you saw was flimsy or could it have been your perception as an undergraduate- perhaps not quite realizing some of the complexity of the topic, design, analysis, challenge of scientifically studying the phenomenon, etc? I ask only because it was a pretty sweeping, dismissive comment to make about published research in any field!
From what you described, and as a professor and published author, I would strongly suggest trying to give a small poster session on your campus. If it has further merit, you may find a place for it at the university level at some point down the road. As described thus far, it's unlikely to be accepted at a major conference, particularly without a strong faculty member backing the work. It would also probably be a long shot to publish in a reputable journal, though probably not too hard to publish elsewhere if all you want is to be able to say "I published something" and don't care how it might be perceived by adcoms/others when you are asked for further details.