First, here is some info from the shop manual...
The perimeter anti-theft feature does not arm until 20 seconds elapses after the GEM receives a lock command and detects all ajar switches are closed. If all switches are closed the flashers will flash and the system will immediately arm.
2001 Escape Workshop Manual
The perimeter anti-theft will disarm only when:
- UNLOCK is pressed on the keyless entry remote transmitter.
- UNLOCK is received from the door or liftgate key cylinder switches.
- ignition switch is turned to RUN (prior to alarm trigger).
- PANIC is pressed on the keyless entry remote transmitter (effective only when the alarm is sounding).
Since you have no transmitters, the symptom leads me to believe that the UNLOCK signal from the driver door key cylinder switch is not getting to the GEM (Generic Electronic Module--in charge of the alarm).
First, I would suggest a simple test, try unlocking the vehicle from the other doors and the liftgate, see if this makes a difference.
Depending on the result of that test, we can determine if the issue is a key cylinder switch in the door or possibly some kind of wiring problem.
Also, you could probably purchase a Ford remote from the internet. There are some specialist sites that only sell remotes, or you could use eBay.
Can you try that simple 'unlocking from the other doors test' and reply?