Looks like the old fuel petcock was a vacuum operated one, someone must have suspected problems with it and replaced it with a generic one. First thing I would do is see that the vacuum hose connected to the old petcock is unhooked and plugged to negate a vacuum leak. A vacuum leak itself could cause it to not start. Another kind of scary thing on there is the usage of zip ties on the fuel lines... They can break without warning, especially if exposed to gas. The one fuel line doesn't really look like fuel hose either. I would take the hoses off and go to an auto parts place to match them up with proper fuel line and get some proper hose clamps. Here is a quicky instructible on carb cleaning to as I am not sure how much you disassembled them. Different carb I know, but the basics are the same for all of them
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http://www.instructables.com/id/Clea...-8-Easy-Steps/
P.S. the quads look good!