TIP: Brief guide to visual electronic fault-finding:

First, IS the appliance plugged in?
IS it switched on?
If YES to above, disconnect ALL power and visually check PCB components for obvious damage or shorts:

PCB: is the Printed Circuit Board burnt?
This indicates that a nearby component has overheated, possibly due to a short-circuit or overload.

PCB traces: are any traces (copper tracks) damaged / blown open?
Traces, the thin copper track 'wires' of the board, can be damaged by shorts / overload / overvoltage or rough handling of component.

Capacitors: are any caps bulging at top more than others, leaking from ends?
This indicates a failed capacitor.
Renew with exact same Farads value and minimum working voltage rating.

Resistors: are any burnt or blown (discolored, holes/ gaps on body)?
Resistors can work as voltage dividers, current limiters, feedback devices or in filters.
All have either screen-printed Ohms values or color-band coding of same.
As the connected 'parallel' circuit can affect a resistance reading, unsolder one leg only then test ohms.

Semiconductors:
Transistors and IC's: Although usually not visible damage, these can fail internally.
They perform many functions, including amplification signal generation and switching.
A very hot transistor / Integrated Circuit "chip" may spell trouble, as heat from overdriving / overloading / shorts may cause the internal junction to fail.
Some are electro-static discharge (ESD) sensitive.
Always renew with same component or, in some cases, an equivalent device may work.

Fuse: As most people are aware, a fuse protects the connected circuit (load) from overload, or over-current in case of shorts, too many devices, etc.
When current limit (Amps) is exceeded, the fuse blows, disconnecting the supply.
A blown glass fuse may have black soot-marks, or loose / blown fuse wire 'floating'.
Besides glass cartridge fuses, there are also resttable PTC types, which look like a disc capacitor, but usually blue.
PTC's open when overloaded, and may take a long time to reset themself, (if at all).

Dirty / oxidized connectors or pads:
May cause erratic and intermittent failures, where signal does not pass through.
Common on "pad" type connectors, as with a ribbon-type 'data' belts used for displays, keypads, etc.
Tactile buttons, common on keyboards, keypads and remote controllers, are also prone to contamination.
Molex plugs & IDC header pins can also become oxidized.
Usually, a wipe with a soft cloth or pencil eraser does the trick.
Surgical spirits or Servisol (contact cleaner) can remove oils / oxidization.

Bent pins: IC's and header connectors may have a broken or bent pin, rendering that pin non-functional.
Pull connector plug out in a straight direction, without twisting, then check all pins are good, before re-inserting any connectors.
Some connectors use a hook / catch system to ensure firm grip.
A small screwdriver, thumbnail or squeeze can unhook the various types.

Rectifier Diodes: usually in the power supply section, maybe individual diodes or a bridge rectifier, (with 4 internal diodes).
This converts AC voltage to DC.
Failure of any diode will disable the appliance.

Potentiometer: is the knob loose, crackling or erratic when touched / moved?
What people sometimes call a 'volume knob', the 'Pot' is actually a variable resistor, consisting of a resistance track, usually carbon, with a center wiper contact.
Often wired as a 'potential divider', the (common) wiper adjusts the resistance inversely between 2 outer terminals.
For example, the wiper may be signal in, the 'minimum' terminal grounded, and 'maximum' terminal out to amplifier.
If wiper or track are worn, signal can be temporarily lost.

LED: is your indication / display LED not working?
Outline of an LED:
As a Light Emitting Diode is polarized, the voltage to it must never be reversed.
This is why the negative cathode has a flat spot on the flange, and positive anode is bevelled.
The current must not exceed the forward current 'If' and voltage through diode must not exceed forward voltage 'Vf' rating.
That is why most LED's have a small 'current-limiting' resistor in series, connected to one of the legs.
A quick & simple single-color LED test using a single 1.5 volt cell and 2 thin insulated wires:
As LED Vf usually begins at 2V-2.2V, we can safely use a singe 1.5V cell without a resistor.
Hold negative wire to cathode side, either on the LED or soldered point on same track.
Briefly touch the positive wire to the anode side, watching for a flash or glow.
Some 2-3 lead LED's may be bi-color, tri-color, or the 4-lead RGB type.
Others may use a higher operating Vf, such as 3V for U/B or 8-12VDC for 'Jumbo' LED's.

Infra-Red Remote LED's: Remote or motor-gate beam suspect? Not sure if working?
Humans are unable to see Infra-Red wavelengths.
The image sensors of most digital cameras, webcams, security cameras, cellphones are sensitive to the IR radiation emitted by the IR-LED at front.
Point your remote at one of these, and watch screen for whitish-purple flashes / pulses of light from the LED.
The pulses are modulated digital data being sent from remote, or for a broken-beam detector, just 'active'.
Also check batteries, and for universals, that pairing is correctly done.
Thassall!! :)