My project referred to a library that had FireDAC components, though I wasn't using any of them. My project uses DBX, not FireDAC, and VCL instead of FMX.
[ilink32 Error] Fatal: Unable to open file 'FIREDAC.STAN.FACTORY.OBJ'
FireDAC.lib was in the project includes in my .cbproj file, so I had no idea what was wrong.
I finally found a fix: drop a FireDAC component (I used FDConnection) on a form. Save all, compile, and it worked. Then, I just deleted the FDConnection from the form and I was good to go.