In August of 2010 I hired a roofing contractor to fix a leak in the roof where my sunroom joins the main house. It was leaking only into the sunroom. We agreed upon a price of $250 to repair the seam. He went up and caulked and tarred the seam. It didn't work. He came back on several occasions after much pleading, and repeated the process. It still leaked. He then told me the leak was due to inadequately overlapped siding and a need for new flashing on the main home above the junction point. He charged me an additional $525 for this, for a grand total of $875. It still leaked. I called and emailed him several times over the course of weeks and had to threaten to call the president of his company (which is locally owned) in order to get a response. He came out and looked at it but told me there was no more he could do. That was in October 2010. In December 2010, I got a letter from his siding subcontractor asking me to pay them because the primary contractor had not done so, and it threatened legal action if I did not pay. It was at this time I noticed I had been charged a 91% markup over the subcontractor's costs. I ended up calling the contractor's boss to complain, and presumably the subcontractor was subsequently paid as I heard no more from them. The primary contractor was unresponsive to my complaints about their charges. I have since hired a new contractor, who found the source of the leak in about 10 minutes, and confirmed that the work done by the previous contractor was not only overpriced, but that the original "repair" of caulking and tarring is a temporary solution meant only to be used while searching for the primary cause of and repairing the source of the leak. My new repairs (which include an entirely new, seamless roof for the sunroom as well as additional flashing) is going to cost $1175. Do I have any grounds to ask for my money back from the original company - if so, how much, and if they refuse, would this case likely hold up in small claims court?

Yes you may ask them for a refund if they did not provide proper service, but caulking and using tar on seams is a normal thing done and on some roofs done regular on some areas where seams meet.

Is the new contractor willing to testify in court that what was done was not needed.

Also a new roof and new flashing is far from a "repair" it is a replacement, and it is most likely that the new flashing was all that may have actually be needed. Or the old room just had some bad placed.