Can a new paper be published with only slight modifications to a published paper?
In computer science, papers are published in archival conferences, which makes things a little confusing. (In many other fields, papers are published in journals, and conferences are just for giving talks -- you can only publish a paper once, but you can give a talk about it many times). 

a) It is unethical, in violation of the rules of the venue, and an incredibly stupid idea to publish the same paper more than once in an archival conference. This is self plagiarism, and is a serious academic offense. 

b) On the other hand, in computer science there are also non-archival workshops to which people are invited to give talks. (These are more like the "conferences" in other fields). It is fine to give a talk at such a venue about a paper that has been previously published elsewhere. 

Your question seems to be whether you personally should commit unethical and stupid act a). I would advise against it. (It is unethical for obvious reasons. It is stupid because anyone who seriously considers your publication record will be sure to spot such a move, and you will not be able to get a reasonable academic job).