The CV still rules when it comes to getting past HR departments and into interview. The HR departments (and employment agencies) I've worked with look directly at the Work Experience section of a CV and then tick off a bunch of boxes for the job they're trying to fill. Unpaid internships are one way to fill a CV with relevant experience. Find a way to bridge that gap and you don't need to do an unpaid internship. I went through 3 months of unpaid work with an ugly little company for exactly this reason, and it paid off, but those were the most trying 3 months of my professional career.