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It's the negative of する、しない. The point missing in the textbook is that this pattern is either 'noun + にかかわらず' or 'verb + opposite verb + にかかわらず', e.g. するしないにかかわらず 来る来ないにかかわらず etc. See also Is "V Vないにかかわらず" grammatical? and http://en.wikibooks.org/wiki/JLPT_Guide/JLPT_N2_Grammar (search for "にかかわらず").
This しない is simply the negative of する; "don't do". The 参加するしない part of the sentence means, regardless (～にかかわらず) of if you participate (参加する) or if you don't participate (参加しない). With this form for "regardless of" (～にかかわらず; also could be ～を問わず), if often takes contrasting or "opposite" ideas. So the 参加するしない is a compact way to list the two choices of ...
仕事に行く is standard for "go to work", just as in English we don't tend to use 'go to the/my workplace', although you might use 'office' as an alternative if you work in one. I think the purpose is implied - you are going to move from your current location to another location, and work there. 仕事場 would be used if you wanted to clarify that you meant the ...
[I've also just noticed this question has come up before (See: Usage of ～じゃん (～じゃない))but you can read my answers anyway - I am going to check them!] Q1: Does "かわいいに決まってるじゃない" mean the same thing as "かわいいに決まってる," just with more emphasis? A1: Yes (but I see from the previous answer it can often be translated as "Actually") Q2: Is the following ...
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