Well, I had a new computer last year - TFT monitor and it was doing the same. Suddenly it'd go off, black, then come back on again. Anyway, in the end, I noticed that although the plug in the back of it was very stiff, it could still work its way out very slightly when I was dusting behind and under the monitor, and also if it was moved, etc. I pushed it in really hard and it hasn't happened since! Sometimes it's only something very small.
(By the way, I always thought you had to have a graphics card of some sort for the monitor?)