Just a follow-up. I performed some measurements on an MJ15003, a straight-up NPN transistor, not a darlington. I got some results that more closely resembled a the cutoff, active, and saturation regions. I only put 15 volts on it through a 1k resistor. I noted what I consider unexpected resuts but within the realm of reason. The device was an open circuit with .388 volts/.83ua B to E. It appeared so be saturated at .591 volts/463 ua, with Vce of .18 volts. In the active region I noted a beta of 52, which is within spec. FYI--I used a 10k resistor in series with the base and the power supply to bias the base.
Now the voltage was quite low as the device is rated for 140 volts Vce, so maybe it would be closer to spec with its normal environment. I was expecting the transistor to be cut off until .7 volts, but by then it was in saturation. Whatever the case, I was glad to see that some actual measurements matched the theoretical ones to some degree. Thanks all for the suggestions up to this point.