SONY KV32S40 NO PICTURE?

While watching TV one afternoon (SONY Model KV32S40), after about 2 hours our screen went completely black. We turned the set off, turned it back on and picture was on again, but shortly afterward it went black again. Repeated off and on process a few times with same results. Eventually, screen stayed black when turning back on. A few days later, we tried the set again, and the picture was back on! However, after only 3 minutes it went black again. The picture quality is excellent while it's on. Is this problem easily fixed or should we trash the set?