Do I need to send the same check or make a new check while resubmitting the GC application which got rejected due to missing documents?

A valid filing fee check must be sent with a re-submitted adjustment of status application, and it does not matter whether it is the same non-negotiated/"uncashed" check initially supplied with an application that was rejected by the USCIS for filing. Especially since you already have been unsuccessful once in your attempt to pursue the often complex application process without legal representation, it would be wise for you to consult an immigration attorney before you re-submit your application. An immigration attorney will be able to assure eligibility as well as the proper preparation of the application package with a full set of supporting documentation. This, in turn, can help you avoid further delays or even more harsh immigration-related consequences.