How do I diagnose a problem with electronic bricks and motors?
I haven't ever used Power Functions remote-control elements, so I can't give you a complete answer from experience, but here are two simple tests:


Connect the battery box directly to each motor, leaving out the remote control receiver entirely. The motors should spin when the light on the battery box is lit, and the slide switch should allow reversing the direction.

Caveat: Looking at the parts list for 42030, one of the motors is a “servo” motor. I don't know exactly how to expect it to behave when connected directly to a battery box, but LEGO's description suggests it should at least move.
Use any camera with a live view or video recording (not an optical viewfinder), such as that on any smartphone, to look at the transmitter while you press buttons. The infrared signal should be visible as a purplish-white dot.

(This occurs because most cameras are more sensitive to near-infrared light than our eyes are, unless they have unusual filtering. This also can be seen with any infrared TV remote control.)




On electrical testing:


  I have not been able to verify function without the battery pack or receivers because I am not sure how much current to apply to an individual motor, 


This suggests that you are confused about how electric circuits work. Outside of specific electronic circuits, you do not choose how much current to apply; the load (here the motor) expects a specific voltage and then draws current according to its needs. (For a motor, the current depends on how much load is on the shaft: a motor not connected to anything will draw much less current than one which is stalled.)

(If you're actually referring to a current-limited power supply, then never mind.)

The voltage for Power Functions is 9 V (or somewhat less), as indicated by the 6 cells in the battery box.

You should be able to apply 7-9 V to the two closer to the middle contacts of the motor's plug (for the simple motors, not the servo motor) and get it to spin. However, it will be tricky to make a connection without the special plug, so if you attempt this be very careful not to short out your power supply. I would suggest not trying it; the battery box should be a reliable power source.

Instead, check the outputs of the battery box with a voltmeter. Between the outer two contacts you should find around 9 volts (for alkaline batteries) or 7.2 volts (for NiMH rechargeable batteries). Between the middle two contacts should be the same voltage, but it will reverse polarity depending on the slide switch.

(Try not to short out the contacts by letting your meter probes touch each other, but if you do, it won't be disastrous: LEGO battery boxes have overcurrent protection. If you do trip the protection then the output will be low or zero for a while before it resets.)