Dear pinguin,
May this find you well. The first thing to check is the RPM (crank) sensor. It is mounted atop the transmissio bell housing, just behind the engine. You can see it from the passenger side of the engine bay, if your sight line is just in front of the air conditioning system dryer (aluminum can right in front of the fire wall). A crank sensor (OM, at www.fcpgroton.com) costs about $35-40.
Crank sensors fail because the insulation dries out and breaks, allowing water to short-out the signal. The fuel pump won't spin-up. Thus, if you put the key in the ignition, and move it to "on", you should hear the fuel pump "spin-up" for a couple of seconds. If you don't hear that, the crank sensor likely needs to be replaced.
Another possibility is corrosion on the coil/ignition power stage (box-like device) which is mounted on the driver's side strut tower. See the FAQs for how to clean the contacts.
As Rex-Regina ignition/fuel management systems seem robust, there's no reason to think about a swap, which would be complicated and costly (replace injectors, engine and ignition computers, wiring, etc.).
Hope this helps.
Yours faithfully,
Spook
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