3D Printers

General Principle of Operation
There are a few different design philosophies for 3D printers, but many of them share the same roots. Debugging and diagnosing printers can be relatively straightforward once you know how all the parts interconnect. The general working principle is a positioning system with limit feedback, a heating element with temperature sensors and extrusion mechanism, a power supply, and a control board running firmware.

Positioning System
There a few a different positioning systems commonly used on 3D printers. This includes Cartesian (XYZ), Delta, and CoreXY. Each of them has their positives and negatives, but outside of this, debugging them is fairly straightforward. If you think you have an issue with the positioning or extrusion motors, you can test this easily by feeding the printer the G code for the axis you believe is faulty. You can find this information easily by reading the reference for your firmware. For example, here is the gcode reference for printers running Marlin. Just direct one of the axes to move back and forth and see if it works. This also works for the extruder as long as there is no filament loaded.

Heating Element/Hotbed
If you suspect the heating element is not working, you are likely right. It's very obvious to tell. However, to guarantee that you're telling the printer that you want the temperature raised, you should reference the gcode and directly send the command yourself (there could be unexpected behavior inserted by your slicer during gcode generation that gets in the way of heating- you never know).

Control Board
The control board is usually a pretty simple microcontroller, but have become a bit more advanced recently. The low end of these boards usually run an ATMega 8 bit microcontroller, but now you can get them running full 32bit ARM microcontrollers. This also houses the driving amps for heating the hotend and bed, as well as the stepper drivers for controlling the positioning system.

Power Supply
These are typically just Meanwell generic Chinesium power supplies. Depending on your printer, you may have a 12V system or a 24V system. 24V systems are generally used for printers that have larger motors and better heating elements- doubling the voltage means halving the current needed, leading to cooler and longer lifespan for the control board. These are easy to replace as long as you can find one with the connector you need to pair it with your control board.

3D Printer Model Specific Information
Lulzbot Taz / Lulzbot Mini Creality cr-10