That's what we're gonna try next. I assume the coil pack should also be replaced at the same time, definitely couldn't hurt since it too looks quite old etc.
and the rest of the story:
1) read and record codes (C)urrent are more important than (H)istory.
2) Clear all codes
3) See what (if anything) comes back.
Click here and follow the instructions that will tell you how to enter the Reatta's onboard diagnostics. Write down any codes that are displayed. Be prepared to write down the codes. They will start being displayed as soon as you enter diagnostics.
Welcome to the forum Ryan. You have already got some good advice. I would like to add that checking fuel pressure would also be a good idea if you haven't done so. Complete instructions for testing pressure and pump performance are in teh How-to guides here on ROJ.
If no codes it could be anything weak in secondary ignition (ICM, coils, plug wires, plugs. I'd switch to a Delco ignition, quality 8mm plug wires, and Delco Rapidfire (platinum) or Iridium plugs.
Padgett is correct in that there are millions in a you pick yard. My testing is this; remove the servo, suck on the large hose and if it doesn't leak, it's good. Never had the electronics go bad. I have 3 Reattas [plus one gone to 2seater]with combined mileage of 950,000 miles and only swapped one out due to seals, never electronics...
I used the cadillac key fobs on my previously owned '92 Rivieras. I scraped the "Cadillac" script off and applied Buick tri-shield stickers to them that I found on eBay.