I don't understand it completely, but I know a little, so I'll share it with you.
First you need to know that "I thought what I'd do was I'd pretend to be one of
those deaf mutes" is a line from J.D. Salinger's book "The Catcher in the Rye." This line basically describes the Laughing Man's attitude after pulling his first stunt (holding the executive of the one micro-machine company at gunpoint on tv). He thought that that single incident would be enough to spur an investigation into the murai vaccine scandal that was taking place. So he disappeared...
When Togusa did his undercover investigation at the clinic, though, he found a similar message written on a locker (I think), which said "I thought what I'd do was I'd pretend to be one of those deaf mutes... Or should I?" This meant that the Laughing Man was thinking about coming out again since his previous actions hadn't had the effect that he desired. Instead, the details of the Murai vaccine had been kept from the public by the current Prime Minister (can't remember his name).
I should have mentioned this earlier, but the Laughing Man had that one cyberbrain disease, which is why he was interested in the Murai vaccine in the first place. When he found out that the Murai vaccine was much more effective than the micro-machines, and that the major companies and the Prime Minister were promoting micro-machines just to make a profit, he decided to do something.
The rest of the Laughing Man case can be described as a struggle between Section 9, who has found out about the power abuses and corruption of the current prime minister, and the Prime Minister, who wages a small war against Section 9 and manipulates the media in order to keep the public from knowing the truth.
FYI, the "Laughing Man" is a short story also written by J.D. Salinger.