Hardware Overview (Atari 2600)
The Atari 2600 has several models. For now I will focus on the PAL Woody version.
The top PCB contains the physical switches, the RF module and the voltage regulator.
Power comes into the top PCB from the 9V DC jack on the motherboard, through the wire harness on pin 2 (usually red wire). This 9V enters the LDO 5V regulator through the power switch on the top PCB and the regulated 5V power goes back to the motherboard via pin 1 (pink wire) and another pin 11 (grey wire) used for the RF power.
The other 5 switches send the pins to ground to signify them being "on". The left and right difficulty setting, the black and white mode, the game select and game reset signals.
The top board also joins pin 10 (brown wire) to ground (DC jack pin 3, main ground pin 6), and pin 11 gives 5V power to parts of the system including the RF circuitry.
These joins are absent on the motherboard, so without the top board the main issue is the ground and 5V signals to the audio and joystick/button hex buffer chip are missing and you will not see composite/RF output after the hex buffer, nor have working controllers.
To bypass the top board completely you can short (pin 10) to ground (pin 6) then short RF 5V (pin 11) to 5V (pin 1) on the motherboard and apply 5V directly to the pin 1 (pink wire).
Pin 3 ground is not important when bypassing as it is only the ground to the original 9V regulator which we are bypassing.
The motherboard contains the MPU (main processor), the RIOT (RAM) and the TIA (video processor) chips, along with joystick connectors, DC jack and various other passive components.

The TIA comes with the markings C010444, C011903, C02871 (on Jr models) or other markings similar.
The other chip (RIOT) is always closer to the cartridge slot and is the same size. The RIOT is marked with C010750, UM6532 or similar.
The MPU is marked with C010745, 6507 or UM6507 as is in the middle and smaller than the other two.