I had the same issue once but I had wired the solonoid (sp?) wrong. I had to swap the two wires around but being this is a new symptom I'd go with the cylinder or a connection that goes to it. Check the plug, I had one once that the p/o had used crimp-on connectors to the back of the key switch
looked like trouble waiting to happen...had to change out the whole harness for that one.
Good luck...