What light intensity determines the start/end of a photoperiod in humans?
It isn't really a specific light intensity that an organism will interpret as the start of a photoperiod. Maynard Johnson reported in 1939 that intensity of light used had an effect on the rate at which mice would shift their circadian rhythms. So, brighter light has a stronger effect, but there isn't a cutoff point that I'm aware of. Johnson was using illumination as low as 2.5 foot candles, which is pretty dim. Aschoff and Pittendrigh did some more work on light intensity in the 50s and 60s, but I don't think anyone ever found anything resembling a cutoff point, only the degree to which intensity had an effect.

Computer monitors are pretty bright. Luminance rating is typically 250-350 cd/m2, which, for comparison with Maynard's experiment, is eqivalent to 23-32 foot-candles. http://computer.howstuffworks.com/monitor6.htm

Johnson, Maynard S. "Effect of continuous light on periodic spontaneous activity of white‐footed mice (Peromyscus)." Journal of Experimental Zoology 82.2 (1939): 315-328.