However, generally the amiga will boot with a bad cia no?
Generally yes, but there are always exceptions. I've repaired one 2000, one 3000, two 1200's and one 4000 in the past that would not boot at all because of a dead CIA. A small percentage of my total repairs for sure, but still possible.
If there is no screen flicker or color at power on, I'm also very suspicious of the health of the CPU. Also make sure the CPU jumpers are set properly. A search should turn that info up quickly.
Plaz