Approach Controller reported a loss of separation between two arrivals; citing distraction caused by a flight data issue and a NORDO aircraft in the area.

Narrative

Before the event occurred; there was a VFR aircraft; Aircraft X; inbound to ZZZ from the north that no one had communication with. I took a point out on the aircraft and the AR2 Controller agreed to work it into ZZZ when/if communications were reestablished. Aircraft Y was inbound from the south and was cleared for the visual approach to Runway XXL. DR3 sector called for a release off of ZZZ1; I told them to hold. Communication was finally established with Aircraft X. Flight data was closed so I asked the Supervisor for a strip on the departure. Aircraft Z was now inbound over the top of ZZZ southbound descending to 6;000 FT. I again asked for the Supervisor to get the departure strip for me; as he hadn't after my first request. He was busy assisting the Controller next to me that had the previously NORDO aircraft. I descended Aircraft Z to 5;000 FT and put him on a downwind. The downwind turn put Aircraft Z on a converging course; co-altitude with Aircraft Y. As soon as I realized the conflict I told Aircraft Z 'turn right heading 180; expedite.' I then went to Aircraft Y and told him 'turn right heading 360.' Neither aircraft took the turns given. Aircraft Z turned somewhat; maybe 20 degrees; then called me again asking what heading. Aircraft Y continued on his present heading. Separation was lost. Less time would have been focused elsewhere if flight data had been open. It took a lot of focus off of the scope having to ask twice for a strip that I should have already had in front of me. Also I think I need to focus a little closer when an unusual occurrence is near.