2007 Lincoln Mark LT 5.4 3v no crank, no start

When you grounded pin 85 just alone, did you try cranking it? Grounding the relay coil windings for too long may not be a good thing for the transistor. I am not too sure about this statement. Hopefully, someone can correct me on that.

Did the test illuminate brightly when you checked the relay control wire? High resistance or a weak driver might make it glow dim.

I did try cranking it and got nothing. Light was bright, I didn't notice it being dim when testing it 12v to 85 and starting it.

I don't really see how a new module will make a difference. It is grounding the relay as it should. A scope would probably show if the driver is weak or not or if there is high resistance in the circuit, which I doubt by the brightness of the test light.
Do you have 12.6 v at the battery? Try checking pin 86 with a fully charged battery and see how much voltage you get? Or you can apply the fully charged battery voltage to pin 86 wire and try cranking it. If that does not work, I don't really know what else to suggest.

Can you try a known good relay?

I opened cover off relay, inserted into fuse box, and measured voltage at pin 86 its 12v constant. With relay out, I doubled checked 85 with 12v from battery test light, I am using a stranded wire with inline fuse, it lights brightly when trying to start. With relay in, cover off, I put 12v test light to actual coil and tried to start, nothing. Why it lights with wire but not actual relay in, no idea. I tried to fatten pin 85 with solder, nothing. I tried bending pin 85 slightly this way and that way hoping to catch the socket, nothing. I rebuilt ignition cylinder, I had the truck in neutral hence it wouldn't let me release key. I received new PCM and programmed new keys, still no crank. New fuse box expected tomorrow.

Would Pin 85, if not grounded, would measure HOT if the switches are in order?

No. Unless you have a short to voltage. Do you have voltage on pin 85 with the key in any positions  other than Start with meter or test light attached to ground?

No voltage on 85 other than ground when in start position. I yanked the fuse box waiting on replacement should be delivered today. I didn't notice anything that stood out maybe one solder joint on board that looked funny but not to the starter relay. I checked continuity from starter relay sockets to back of board solder joints, everything checked out. I noticed on scanner that when I put it in START position it commands starter solenoid ON but there's an option to recognize key in START 3 position either off or on, it stays OFF when I try to START. It recognizes key in OFF, ACC and RUN but not START. It's new ignition switch aftermarket. Not sure if that means anything so I went back to the remote start module with the three inline fuses that were connected to ignition switch, the one that blew was to the ignition red/light blue wire that goes to starter. Since I had the fuse box out, the access to the connectors to junction box easily accessible, I did a continuity test on that wire and two other wires light green/violet and blue/green both check out fine. I did try different known good relay, swapped, and I even bought a new one, still the same results.

It is a simple starting system. When the key is in the START position, you should get power on pin 86 providing that the NSS and the ignition switch are good and ground from the PCM if you have the right key and the PATS is not acting up. Power on pin 30,which allows current to flow to the starter once the switch is closed. We know that we don't have a power and ground issues to the starter, reason is that the vehicle starts when you manually close the switch.
You also have good power on pin 30.  You have everything for the vehicle to work: power to pin 86, ground on pin 85, power on pin 30. 
The only thing you could do is to carefully wire all the wires to the relay and try to crank it. If it cranks,you will know that the box is the problem 
I advise against that. If the wires are touching each other, you can short things out and even fry the computer. 

Got it!!! Can't believe I missed this. There's an additional starter relay in engine compartment named auxiliary relay box labeled R01 it's a 5 pin plus I found melted diode. Hallelujah

Glad you found the problem. Hopefully, you can return some of the parts that you have purchased.