Isolated mains sensor
The mains isn't a floating AC source, one side of the mains (the "neutral") is tied to the general mass of the earth and to the protective earth connection on your socket.

Your laptop most likely is floating, it is certainly floating when running off batteries and is probablly floating even when plugged in (most laptop power bricks are floating output).

Your dads desktop on the other hand most likely has it's ground line tied to the protective earth on your socket.

Now look at those diodes on the left side of your schematic. When you plugged the device into your dads desktop then on the negative half cycle of the mains current flowed.


From the protective earth connection on the desktops plug.
Through the desktop's power supply to the DC ground of the desktop.
Through the ground line of your signal cable to your board.
Through one of the diodes on the left of your scehematic.
Back to the mains.


The current flow would have been substantial. Likely the resistance of the path was less than an ohm leading to an initial current over a hundred amps. 

BANG

Your laptop is floating, so there was no bang but there would have been a significant electric shock hazard if you touched a metal part of the laptop at the same time as touching something protectively earthed.



So you want to build a mains voltage monitor that doesn't blow things up. There are a few of approaches.


Use a transformer up front, to both isolate the mains and reduce the voltage to a safe level. 
Use a linear optocoupler in combination with a capacitive dropper.
Make your circuit referenced to the mains and then isolate it's signal lines using optocouplers. 


All are feasible in general. The first is probablly the easiest and safest for a beginner as the only thing connected to the mains is the transformer primary. The downside is that the upfront transformer is likely to be relatively bulky and expensive.

The issue with the second approach is that gain repeatability of optocouplers is apparently poor, you can work around this by "servoing" them but that comes at the cost of much more complex circuitry on the mains side.

The issue with the third approach is that you have a bunch of circuitry on the mains side. This circuitry will need to be powered (more components) and programmed (be careful you don't create a hazard by connecting the programmer).