No, there is no reason for your to have CRA training. Of course, for your skill set, I do not recommend applying for CRA positions, but instead positions in data management. Your greatest asset is your technical skills in software and your BS in biology. You'll have to really re-work your resume to make it tailored to clinical research needs, but there is no reason why you won't be able to get started in the field.
If your resume answers these questions, you are golden: Have you worked with databases/EDC/EMR systems? How can you improve software to make data collection more seamless? Do you have a strong attention to detail? Do you have basic medical knowledge? How can you improve the accuracy of the data entry and validation systems?
New Jersey is a great spot for CROs and pharma companies. Look for positions in Pharma with 'Software Engineer,' 'Data Manager,' 'Database,' 'Systems Engineer,' etc.