Sometimes I would have to turn the key a couple of times before it would start.
When you say, 'Turn the key a couple of times', do you mean crank the engine, then let it rest, then crank the engine some more,
Do you mean you had to hit the key two or three times before the engine would start cranking, Indicating a bad ignition switch or linkage?
I replaced the solinoid and now there is a short issue somewhere so I don't think the solinoid was the issue. There are three wires going into the once side of the solinoid, (battery cable is okay, wire to alt is okay, other wire is okay except when I turn the key it reads as a groud).
How do you know the 'Battery cables are OK?'
The only way to test the battery, and indeed the battery cable, is with a load tester.
In fact, you should load test all the starter & battery cables...
The wire going to the alternator 'BATT' terminal should read as an open circuit since the diodes are not going to let any current pass...
Unless you have the 'Sense' wire looped from the two wire plug around to the 'BATT' terminal, then it's going to read as a 'Ground'.
The second small wire will read as 'Ground' since anytime the ignition switch or lights are on, any current applied will be going to 'Ground' through what ever appliance or accessory.
If I detach the little ignition input wire from the top of the solinoid and send 12v into it straight from the battery with the wire reading as a ground disconnected the jeep will turn over.
If you mean you jumper power from battery to the 'Lite Blue' wire terminal, or the 'S' terminal on the starter relay, that means the starter relay is working correctly,
As are the battery & starter cables.
Did you test for 12 volts from the 'Lite Blue' wire when the key switch is in the 'Crank' or 'Start' position?
If you have 12 volts, then the starter switch is working.
If you DO NOT have 12 volts with the key switch in the 'Crank' or 'Start' position, then you have something wrong, mis-adjusted ignition switch linkage, bad ignition switch, open wiring, ect. between switch and starter relay.