So I have afriend who has a 86 si civic hatch well, I just put a new radiator in it for her and and got it running but now a week later a light that reads "PGM-FI" is coming on and going off here and there what would this be caused by?

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It's the CEL indicating a fault with one of the sensors. Here's how to read the code from the ECU:

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DIY 92-00 Civic Check Engine Light (CEL) http://www.honda-tech.com/zerothread/1901557
Manuals http://hondatech.info/downloads/Auto/Manuals/Civic/
97 Civic DX sedan, D16Y7 MT --- 00 Civic EX coupe, D16Y8 AT