You have the later vacuum powered petcock type. It won't flow fuel in the "ON" and "RES" (Reserve) positions unless the motor is running, or at least turning over so it supplies a vacuum signal. There is also a "PRI" (Prime) position. This flows normally and needs no vacuum signal. You use this if the carbs have been drained to quickly refill them. The position you're in is denoted by which way the end of the lever is pointing. Straight down is "ON", forward is "RES", and back is "PRI". There is no "OFF" position on your petcock but "ON" and "RES" can be considered as such since they only flow with the motor running. Don't park or store the bike for long periods with the petcock in the "PRI" position like it is now. The carbs can over-fill and leak fuel all over the place.
It's really not a good idea to try and start a machine that has sat for a long time without first looking into the carbs. At the very least, take the float bowls off. If the gas wasn't drained before the bike was parked, what was in the carbs has probably evaporated away, leaving behind gunk and varnish. Try to start it and you'll suck all the crap into the carb and plug it up. Catch it before that and all you may need to do is clean out the float bowls. You've been warned.