We never use the petcock on radiators with plastic tanks. Chrysler had a big problem in the mid '90s with their radiator supplier. Once the petcocks were opened, something cracked that the o-ring sealed against and you would have a drip about once every five seconds. The only fix was to replace the radiator. It often took weeks to get a new one because of the backlog of orders. Since that experience we never use them. We just pull the lower radiator hoses off, which is usually easier anyway than trying to reach an inaccessible drain.

It's hard to say without seeing it but it sounds like your petcock may be broken into two pieces. You turn it 1/4 turn, then pull it out. It will be about 2" long. If it's broken, all you'll get is the handle that's about 3/4" long and there will be no o-ring on it.