JFK Controller described an airspace deviation when traffic was issued a turn direct to a NAVAID that was not operational; the reporter indicating the status of NAVAIDs should always be available to operational personnel.

Narrative

While training someone on Local 2; a Heavy B767 was catching up to a Heavy B747 on the final; so he was told to cancel his approach clearance and was instructed to go around when he was 7 mile final. He asked me what speed I wanted and I told him it was his discretion. The B747 decided to go around on short final; and was instructed to turn left heading 220 at 2;000 and the B767 at 3;000 on runway heading. The B747 went around at the last minute. The B767 was told to expect a left turn direct CRI VOR in 1 1/2 miles; when he was 2 miles south. I turned the B767 when he was 2 miles northwest; but he never turned; which led him to enter LGA's airspace. LGA had a B757 on final for Runway 4 at 3;000. The RADAR collision alert sounded between my B767 and LGA's B757. I issued the traffic to the B767 and he said he was IMC. We later found out that CRI VOR was OTS and that is why the B767 most likely did not turn when I instructed him. Have someone monitor CRI VOR so we know when it goes OTS in advance. N90 Final Approach gave us the planes with the loss of separation; next time separate them before you gave them to Tower.