My car would not turn over when I placed the key in the ON position so to see if it was just a loss of power from the battery to the starter, rigged a wire from my fuse box to the male clip on the starter, so when I close the circuit of the one on the starter and the one attached to the fuse box the starter juices up. This worked up till a few days ago and I went and bought a new starter because the old one failed the tests at Autozone. The new one, however still does not work properly without the wire rigging as before. My battery cable did not indicate a voltage drop, and the battery itself tested fine. What could my problem be??

Your problem is in your starter control circuit. Possibly a bad relay, neutral safety switch, or even a bad ignition switch. Get ahold of a wiring diagram for your vehicle and check the starting control circuit components with your voltmeter.