I examined the live url you have provided and the first thing I noticed is that there is a js error thrown - the function attached to onload and onmouseover events which is the following one:
is undefined. This is most probably not the reason for teh problem, but please fix this first because when you get a js error unexpected behavior occurs and this should be first resolved before continuing to examine the setup.
As to your question - yes, it is possible to define the WebService and WebMethod in the code behind of the same page instead of a separate file as far as you follow the same logic and you have the needed attributes set.
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