Enroute Controller described a confused event when traffic landing at a non-Towered airport failed to acknowledge receipt of NOTAM information only to discover the landing runway was NOTAM'ed closed.

Narrative

A BE20 was planning to land at ZZZ and did not know the runway was closed until he was very close to the airport. He was on an IFR flight plan when he checked on and after requesting a visual approach; I asked if he had the weather and NOTAMs. His response was; 'Yes... (pause) we have the weather.' When he was about 5 miles from the airport he said he had the airport in sight and canceled. About 2 minutes later; he was trying to call me; but could not hear my response so I had another aircraft ask him what he needed. He asked if ZZZ was closed because he wasn't showing it NOTAM'ed. I immediately looked at the status board and it only showed another airport's runway closed and advised him that I was not showing it closed; but would research it further. So; I pulled up the NOTAMs in ERIDS; but he was also asking for a close airport; so I advised him that two other airports were closed. I finally read the NOTAMs in ERIDS slowly; because I'm not accustomed to reading them; and found out that the runway at ZZZ was indeed closed. I observed a 'V' target flying around ZZZ and assumed that was him; but I wasn't getting any more responses from him; so I'm not sure what happened to him after that. I should have prompted him to read the NOTAMs or read him the NOTAMs when he responded that 'he had the weather;' but didn't specify that he had the NOTAMs. However; that detail should have been posted on our status board and detailed during sector briefings throughout the day. As a Controller; I think we need to either learn how to read NOTAMs more easily or NOTAMs need to be easier to read. It did not reflect well on the FAA that we didn't seem to know if an airport in our own airspace was open or closed and no one in the area knew; and as a group effort; it took us 5 minutes to find out.