Welcome to the forum!
The PATS light normally blinks slow (even with no key inserted) and then blinks rapidly if the right key chip is not detected when you try to start it. Is this what is happening?
There is a lengthy topic on this forum linked below, or you can program in keys (starting with none or only 1 since the owner's manual method requires 2) using an ELM327 based OBD2 dongle (for example a BAFX on amazon) linked to a windows host device (like a tablet or laptop, USB, wifi, or bluetooth linked depending on dongle and host connection capability) to run Forscan app. Forscan also has an android app but I think only the windows version can program keys and "might' require the full license which you can request on Forscan's site.
Antitheft and Alarm Systems: Description and Operation ANTI-THEFT The passive anti-theft system (PATS) uses radio frequency identification technology to deter a driveaway theft. Passive means that it does not require any activity from the user. The PATS uses a specially encoded ignition key...
www.explorerforum.com
There may be newer related topics on forscan's forum, or even youtube videos showing the process.
While this does require the OBD2 dongle, I would highly advise getting one if you don't have one because this can save a lot of money and gray hair in making an older vehicle more cost effective to keep running well. Forscan is the preferred app, has far more Ford specific features than more popular OBD2 dongle apps like Torque.
If it won't reprogram the keys at all, it could be that your PATS transponder module in the steering column, or the wiring to it is damaged. You can take the column cover off and inspect it but if nothing obvious is seen, then it becomes more apparent when trying to program the keys, that it can't see them to program in at all.
There are other potential faults like bad wiring, connector to, or the ECU itself but these are less likely, so basically I've mentioned things in the order I would try to resolve this.
If the programming attempts don't work, another useful resource is the wiring diagrams linked in my sig below. Keep in mind that some parts like the transponder, might be very inexpensive from a junkyard or junkyard pull on ebay/etc, but pretty expensive to have a dealer do for you or even buy the part new.
Before I towed it to a dealer, I'd call a few locksmiths as some will be mobile, have the ability to come on-site and program in keys, but be sure to mention that it's a '98 with PATS2, doesn't recognize ANY keys currently so they know they have to have a dongle or scan tool/appliance to program the keys instead of just doing what is in the owner's manual or cloning a working key. Depending on the area, this service is roughly $200... bound to be cheaper than a dealer + tow charge.