Lost my keys drilled out the ignition, need to bypass PATS system

First off, Welcome to 2CarPros.
I have yet to see a "universal bypass" work when the vehicle uses a transponder key as yours does. From the description it sounds like you will need a few parts. The transponder antenna, that's the ring with wires that came off. That isn't a programmable item so a used one would be fine. Next you will need a replacement ignition cylinder and at least two keys that operate that cylinder and can be programmed into your anti-theft system. That as well could be a used part however if you opt for a new one it could be pinned to match the original key which would allow you to use the original door lock without a different key.
Remove the bypass box and hope that it didn't damage anything in the anti-theft system.

Replacing the transponder antenna isn't that difficult. Disconnect the negative battery terminal. Then remove the tilt column shaft by twisting it and pulling out. Next remove the three screws from the lower steering shroud on the column. Next might be the hard part, If you drilled the old cylinder did you remove it? If so then good. If not you will need to see if you can rotate the cylinder to the run position, then push the release in with a punch to pull out the entire cylinder.
Next is to carefully pull out on the trim cover above the column, This can be tricky as the plastic tends to get brittle.
With that cover off remove the upper steering column cover. Again this snaps on and the tabs like to break.
Now you have access to the transponder module. As your's is already broken you just need to remove the remainder. There is a screw underneath and the tab on top. The wiring then unplugs.
Installation is done by reversing these same steps.

The replacement keys now need to be encoded to the vehicle. Ford has a process for this without a scan tool, I've tried it a few times and only had it work once so I now use a scan tool every time.
However here it is if you wish to try it, it will program a single key into the system. There is a different procedure to add a spare key.

Primary Key -
1. Insert the non programmed key in the ignition and turn to RUN.
2. THEFT indicator flashes rapidly.
3. After 15 minutes of flashing, the THEFT indicator will stop flashing.
4. Within five minutes after the THEFT indicator has stopped flashing, turn the
ignition key to OFF and back to RUN.
5. After 15 minutes of flashing, the THEFT indicator will stop flashing.
6. Within five minutes after the THEFT indicator has stopped flashing, turn the
ignition key to OFF and back to RUN.
7. After 15 minutes of flashing, the THEFT indicator will stop flashing.
8. All originally programmed keys are now erased, and only the key in the
ignition is programmed.
9. Attempt to start the vehicle. It should start and run with the THEFT
indicator proving out after two seconds.
10. Additional keys may now be programmed.

Spare key (or more) -
1. Insert the programmed key (from the above steps) in the ignition. Turn to RUN.
2. THEFT indicator proves out after two seconds.
3. Remove the programmed key.
4. Within 15 seconds, insert the new key in the ignition and turn to RUN.
5. THEFT indicator proves out after two seconds.
6. The extra key is now programmed.

Watch the times they list in the process, if you miss one of the windows to move the key you have to start over. I have seen times that it worked only after four times but in the event it doesn't work an automotive locksmith or shop that has the proper tools can use them to program the keys.

You're welcome. If you run into trouble we'll be here.

This will not work unless the keys are already programmed into the system. To encode new keys you need a scan tool.

The keys have a chip in them. The scan tool is used to tell the security system to scan for a key. It sends out a pulse that powers the chip in the key. The key sends out the code it has in it and then the scan tool user verifies that it is a valid key. The security system then stores that returned code as valid. The second key is done the same way. Once you gave two programmed keys you can add a third key without a scan tool. However, there is no way to do that on most cars unless you have a scan tool or key programmer to enter the keys into the system.

To do a couple keys it would be much cheaper to have a locksmith do it. A scan tool that can program keys starts at around $200.00 and goes up from there.

You actually cannot remove it. The system is built into the instrument panel and BCM and PCM as sections so that a criminal wouldn't try to remove it. All the pieces talk over the data buss to ensure they are all there and functional or the engine doesn't run.

I know it's an 2001. The thing is Ford uses different security systems between the trucks and cars and even different ones based on the car lines. That is why the Expedition method doesn't work. As for the online programmers, I cannot say if they work or not. I know many of them work with the Euro and imports okay, but fail with the domestics. However a locksmith is still likely going to be cheaper overall. The ones around me get about $40.00 to program two keys. Whichever you choose to do, good luck.

Lets do a Ford security reset. please follow this guide:

https://www.2carpros.com/articles/how-to-reset-a-security-system

Please run down this guide and report back.

The only thing that may work is this. Turn the key to the run position and let it there for 10+ minutes. If the theft light goes off, it should start. If it doesn't, the only thing you can do is have it towed to a dealer to have the damaged parts replaced and reset so the computer recognizes the new key, cylender.

I mentioned a dealer because they will be the only ones with the right equipment to check the system to diagnose where the problem is located.