Avoid rewiring much of anything till ya troubleshoot. I don't have much experience with the E4od sensors for some reason. haha. guess not too many rigs with this transmission have come my way. On that note, we need more info to help. Questions i'd ask off the bat...
#1, What was wrong before any service was done? Crank but no start? or it started fine but had shifting issues?
#2, What did you rewire? sounds like it wouldn't crank after the fact and you jumpered the solenoid to get it to crank/start?
#3, you say it's not shifting, as in the gearshift handle does not move? or is it more like you do have drive and reverse, but as you move down the road it's not shifting as it normally would? (acting like you just took the shift handle all the way past drive 3 2 and down to 1)
From what i know off the top of my head, it seems that this switch may be easily installed out of alignment, and is somewhat adjustable, even when installed correctly. there's a line painted on it which indicates NEUTRAL position. if the switch were installed while in PARK position, it may not be in the correct position whatsoever. Furthermore, the switch may be preventing the shifter from moving into drive if it were reaching it's (misaligned) limit...
Was the transmission in neutral when installing the switch/was the neutral position painted line on said switch lined up on the sensor when installing it? if you are certain of this, than it seems the questions above would help us get to the next step of troubleshooting.
Welcome by the way, i'm seldom on here, but figured i'd throw my 2c here.