scrambled screen and totally frozen system (internet related?)

Alright, here's my photo for you:

About the Freeze: Nothing is responsive when the screen gets like this. The computer becomes very quiet, so it's definitely stopped processing anything. That cursor isn't movable or animated, by the way. I do a hard restart when this happens and the computer runs without any trouble afterwards.

Circumstances for Occurrence: This usually happens when the computer is in the same room as another computer connecting to the network. (It's fine if it's in a different room.) It can be in the same room as a desktop computer without problems after connections are complete, but not during connection. Being in the same room as a laptop sharing the same network however always leads to this, usually within seconds of entering the room. Laptops on different networks don't cause problems unless they are placed very near my laptop. Sometimes this also happens when transferring files over the local network, but this is not consistent. There is also a 100% rate of occurrence when I try to run any MMO games; it happens as soon as the game client launches. All other software functions correctly, including other internet-dependent programs.

Computer History: All of my problems are recent. The laptop is about 2 years old. It was dropped two months after I bought it, and the plastic case broke off on the corner by the power button, but everything continued to work as normal. Recently, on of the wires connected to the power button got snapped, and the computer must be turned on by bridging the connection with a metal tool while pressing the button(the wire and it's contact point are too small to solder safely.) I have been keeping the computer on since then, plugged in and in sleep mode most of the time. My scrambled screen problem has only started happening since that wire snapped.

Troubleshooting: I tune up my computer every week, and have not had any issues with viruses or malware etc. Hardware diagnostics claimed that my system is healthy. I thought of  plugging in an external monitor to see if the problem would appear there as well, but I do not have a cord to do so. If it would help you diagnose my problem, I'd be willing to go buy one. I've made sure that all my drivers are up to date, and I did try restoring the system to its state before the wire snapped. There hadn't been any new software installations during that time, though. I have tested this on two different networks and both had the same results. I haven't taken a look inside my computer yet, but I'm certain there is a physical problem.

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