Detecting cancer or a genetic predisposition based on DNA sequencing
When sequencing a human's (i hope im stating this correctly) genome is
  there a difference between the genome before and after the patient is
  found to have developed some sort of cancer.


If you are asking if cancer cells have an altered genome as compared to the rest of the organism, yes, this usually is the case.


  What would be a method for determining whether or not a patient has
  cancer based only on a genomic-sequence.


If you scrape some cheek cells to do DNA sequencing, you will know what the sequence is in those cheek cells, and you can figure that most of the cells in the rest of the body have that same sequence.  But if some, say, brain cells have acquired genetic errors causing them to start going haywire, that won't magically change the DNA in your cheek cells.

A genetic predisposition could be identified...if scientists had determined one.  For instance, Angelina Jolie got a double mastectomy because both her family history and her genetics strongly indicated that she would get breast cancer otherwise.