No Start / No Shift Case 580K

Good Afternoon! Been a while since I last posted anything on here, but I am at a complete loss and am hoping that I can find someone who might be smarter than I am. So, I have a early 90's Case 580K loader/backhoe that I have owned for about 6 years. Overall, good and reliable machine with exception to a few things. Earlier this year (April), I was using it to build my new house, and parked it next to the field. Well with winter coming, I figured I better get it back to a more "work friendly" area, and went to fire it up. However, she didn't start at all. I thought the batteries were dead, but they had plenty of juice. I thought perhaps the neutral safety switch was in the wrong position, but it wasn't. Nothing, I could not get anything to work. So I checked the voltage across the wire that comes from the battery to the key switch and it was only showing 6 volts... Hmm... Checked battery voltage, sitting nice at 12.8V on both. I thought that perhaps the wire was busted from a critter, somewhere in the harness. So, I ran a temporary wire from the battery to the battery post on the ignition switch to see if it would start, and sure enough, it started right up. If I removed it, it would of course die out. Okay, bad wire, no big deal. So I had my son jump in the machine with me jimmy rigging the wire in place, and it would not shift into either forward or reverse. I checked the oil level, it was low, so I added more to it. Tried it again, and nothing. No forward and no reverse. Took a look at the linkages, and everything was working as it should. So here is my question. I have read in other threads that the neutral safety switch is operated off of hydraulic pressure for the transmission? That doesn't make much sense to me, so how exactly does that work? Could that also be the reason I cannot get any forward / reverse movement? Does anyone have a hydraulic schematic for how the transmission is supposed to work? I sure would appreciate it!!