So, I've got myself a 1996 3.8 V6 that won't start.
No rapid, repeating clicking, no turning over, nothing. Power comes on, but after i turn the key past giving power to the accessories, everything shuts off and you have to pop the hood and fiddle with the wiring to get the accessories to power on again the next time. I've changed the relay, the coil pack... Nothing. The battery shows a full charge and i can't find any loose wiring. Anybody got any tips?

 

If wiggling the wires got the accessories to power back on,thats usually an indication that a cable or wire is loose,corroded,broken internally or shorted to ground.Ground cables & wires should also be checked.If your battery cables arent the factory type cables,with the battery cable terminals that are built into the cable,& they've got those cheap parts store bolt-on type terminals,they have to be super super tight to work & they loosen up quite frequently.If the starter wasnt turning over,but the accessories were continuing to remain on once the key was turned to the start position,I would suspect the wiring to the starter or any other part of the starting system to be the most likely culprit.However, since the accessories are cutting off instantly as soon as the key is turned to start,a loose/corroded battery cable or ground,a broken cable terminal or low battery voltage seems more likely.Check the battery with a multimeter by placing the leads across the battery posts.It should have 12.6 volts fully charged,key off/key on.It should have a minimum of 12 volts.If its below this value,the battery needs to be charged on a trickle charger overnight.
Since the starter puts such a high load on the battery at startup,it can pull the battery down by several volts at startup.The minimum cranking voltage needed is 9.6 volts at a 70° ambient temp.This minimum value can drop by 0.1 volt,for every 10° of ambient temp drop,and it will still be enough to crank the engine.
70°= 9.6
60°= 9.5
50°= 9.4
40°= 9.3
30°= 9.2
So if you hold multimeter leads to the battery posts while someone cranks the engine (disable the coil for this test) and the meter reads less than the value given in the list above @ the temp shown,the battery doesn't have enough reserve capacity to power the starter to turn the engine over.If this is what occurs when you run this same test on your battery,recharge the battery overnight and try the test again the next day.
If you can get the no crank condition figured out & then you find that the engine will turn over but it just won't start,we can start at that point and trouble shoot that problem.