I have found GIS shape files from the following link: http://elections.il.gov/votinginformation/2011congressionaldistricts.aspx What would be the easiest way if possible to process/tool that I need so that we can map/lookup the list of zip+4 codes to the shapefiles to find the senator and representatives name, address, zip, district and county.
For some sense of why folks aren't thrilled about your question check this thread: Looking for ZIP+4 boundaries
Zip codes--especially the nine digit variety--are not easily transcribed in the way you would like (They aren't polygons and the routes frequently cross district borders). One approach would be to use 5 digit zip codes (see also Most Up-To-Date Source for US Zip Code Boundaries) which might be a bit better (although some 3000 zip codes cross district boundaries nation-wide). Even then, you still basically need someone to just do it for you since you have no software or software familiarity.
For what it is worth, what you are asking for is possible in R, QGIS, GRASS and several other open source projects, but with your level of knowledge it is likely more efficient to simply purchase a database. Search "zip codes by congressional district" for multiple options. I found the summary here: http://askville.amazon.com/Easy-free-online-identify-zip-codes-Congressional-District/AnswerViewer.do?requestId=14537568 to be sufficient.
Given the simplicity of putting together this file in rudimentary form someone may be inspired to make a free version (it might even be me), but for now you are stuck I think.