May I ask? What were the original symptoms leading to the replacement of the starter and solenoid? Did the engine simply rotate a few degrees and then stop when you turned the key switch to start the engine? Is this same behavior that you are continuing to get?
If so, the valves need to be PROPERLY adjusted to restore the compression release feature that your Briggs Vanguard engine needs in order to crank properly.
If this is what you are experiencing, and you are handy at DIY stuff, we can get you through a valve adjustment.

If the starter turns over when connecting jumper cables to it but doesnt turn over at all when connecting the jumper cables to the tractor battery I would suspect a blown fuse. There is most likely an in-line automotive type fuse in one of the wires coming off of the ignition switch. If that is good, then the next question is does the selnoid make a clunk sound when you turn the ignition? If not then you somehow either got a bad selenoid or have a broken wire somewhere.

One other possiblity. You are sitting on the trackor seat and pushing in the brake/clutch when you try to start it right? There is a deadman switch that will keep the ignition from firing under the seat and there is another deadman switch that will keep the starter from engaging if the brake/clutch isn't pressed all the way in.

Keith