If its just about getting webpart content from an accessible page within same domain, I dont think you will need a webservice for it.
You can place your webpart within a div (id=container) and use below Jquery :
When this method executes, it retrieves the content of sitepages/test.aspx, and then jQuery parses the returned document to find the element with an ID of container. This element, along with its contents, is inserted into the element with an ID of result, and the rest of the retrieved document is discarded.
If you need to access content of webpart on page outside the domain, You use
contents() jquery function as mention here:
In any case, if you are determined to go for the webservice, you have to code for this. In the webmethod, you can parse the page and return the content of the html sections you need by using HTMLAgilityPack