Did I overheat my Arduino while soldering to perfboard?
I would like to clarify that my only question in ENTIRE post was: "Is that enough to break the board?" 


The answer to that narrow question is that heat from soldering with an iron is extremely unlikely to have done this.  IC's are in practice (vs data sheet) quite heat tolerant, and further the pins you are soldering on are not even the pins of the IC or any electronic components, but rather those of the module headers.  You'd be more likely to melt the plastic web between those headers pins, but even that won't be a great problem since they are already in place. Or if you were soldering directly on the board, lifting a pad or trace - but you were not doing that.

Your actual problem is something else, what that might be is presently unanswerable due to the lack of detail in your question.