Is that a new cylinder or did you put the old one into the new switch assembly? If it's an old cylinder being reused, why were parts changed? What was the previous problem? A common cause of everything else working except for a failure to crank is a cracked cam on the end of the cylinder. When it's loose, it won't turn the switch quite far enough to hit the starter contact. The dealer's parts department has a simple repair kit for that.
For other symptoms, most tests can be done at the starter relay socket with a test light or voltmeter.
Wednesday, July 13th, 2011 AT 8:15 PM