Tested ADC with just voltages - it's working fine. The problem before may have been a common ground or other voltage problem. I've put in an order for 2.5V regulators so we can scale the weight sensor voltage outputs properly. Once I get that regulator I can test the weight sensors properly.
I now have the Ethernet module initializing properly. Problem was a combination of bad arithmetic (forgot to multiply by 4 to convert from byte-shift to bit-shift, and also had a bad value) and the Wiznet module's big-endianness. My laptop can correctly choose between crossover and straight-through cables, but I'll hold on to both for now in case whatever device I use later can't make the distinction.
Next time (probably Sunday or Monday) I can start looking into writing DNS and HTTP stacks.