Experience moving from back office role to Investment Banking or something similar

I know this has been asked before, but I have a somewhat unique background. I graduated last year from an Ivy League school as an econ major and currently work at a hedge fund in a back office role. It is relatively low stress and hours are good, but it isn't interesting to me and the pay is mediocre. I have a background in the military and transferred to the Ivy from a lesser-known school. Most of my credits were counted for the credit minimum for graduation, but did not go toward many of the requirements, so I spent the summers taking classes instead of interning so I could graduate in 4 years. Looking back, that was a boneheaded decision but it is what it is. Senior year rolled around and I did not have an offer, so I took what I could get. My interest always was in banking, but as you can imagine, getting a full time offer without internship experience was nearly impossible.

If you have experience in banking and/or have made a transition like this, I would be interested in learning your thoughts on how likely it would be and any advice you have for doing it. MBA is pretty much out of the question because my GI Bill is pretty much depleted and I don't want to have to take on the amount of debt necessary to finance it.