Are you a NY state resident? Instate Tuition is ~$6.5K per year! Is it possible to apply to a non-engineering major at CCNY and then transfer into the ME Program after a semester at CCNY? If you are NY Resident, what about SUNY-Stony Brook/Binghamton University? Manhattan College (with good financial aid)? Rutgers University (if NJ resident)?
With 110 credits, you are close to the 120 (131 for ME Degree at CCNY) degree threshold. I not sure CUNY or SUNY schools penalize students for excess credits beyond a certain percentage of the degree requirement, but I think you should at least attempt an appeal, possibly meeting with key individuals at CCCY Grove School of Engineering.
Why did you abandon your business/finance degree? Maybe that route might be your best option, especially if you minor in computer science or Computational Finance/Financial Modeling.