If the CIAs are the problem, you'll still get 5V on the 5V rails to the various parts. If there's a short in the power rails, the 5V will disappear or drop below maybe 4.5V. I can't see it being any other lines that are shorting because nothing else on the joystick ports would cause a failure to boot like that.
The CIAs are U300 and U350 on an Amiga 3000. The schematics are available
here, which might help you out... The chips themselves have the same functionality as they do on every other Amiga (bar the CD32), and AFAIK the chips are the same part as on all the non-SMT Amigas (1000, 2000, 500, 500+, CDTV).