I did some more reading and investigating last night. The chip on the Tadao board is a power MOSFET (transistor) (
LR014N).
This page explained its need/use in the circuitry.
This page explained the need for the diode.
From what I've read, the microcontrollers don't have enough amperage to power the solenoid directly. So you hook up the pin on the microcontroller to the MOSFET and then hook the MOSFET up to the main power and solenoid. The MOSFET then acts like a switch, and when the pin triggers it, it powers the solenoid. The diode prevents any reverse voltage from frying the microcontroller. I get the general concepts, but I'm going to do more reading in my
electronics book so I can fully understand what's going on there.
I found some suitable S1A diodes on eBay for relatively cheap. I haven't found anywhere online to order small quantities of the LR014N MOSFET (or other equivalent 55V 10A devices), unfortunately.
However, turns out there actually is still at least one electronics store here in MA. I'm going to go to
You Do It Electronics sometime this week and see what I can find for MOSFETs. I may check my local Radio Shack first, but I highly doubt they'll actually have anything useful.
I'm glad I was cautious about the noid and didn't just hook it up. I probably would have nuked the noid or the board if I'd tried it. I'm definitely at that point where I know enough to be dangerous, and am trying to understand things fully before I try to implement them.