1993 Cadillac Seville Baffled!

I have a 93 Cadillac Seville. Replaced starter solenoid about a month ago. After I replaced it the car would not start via the key. I was in a hurry and ran a hot wire to the post of the solenoid on a toggle switch so my wife could get to work. The car would also start by jumping the posts on the starter. However it would not drive very well, cutting out and stalling. I found that by turning the key to the coil position and leaving it there it would run fine. A few days later the battery died and she bought a new one. The day after I was troubleshooting the starter system and after hooking everything back up correctly the car started and ran with little to no problems.

Yesterday the car would not start upon returning from a store. I tried jumping the posts but the new battery was dead. The water was low so I added some, and after letting the car sit and getting a jump it started but I was back to having the problems with it cutting out just like when I had the ignition system bypassed via the toggle switch. I can also turn the key to start but only in drive because it fires the starter in park and neutral and it runs well. The alternator and battery checked to be good and I don't understand how the coil positon will line everything out.