Sorry for the confusion. It has been a long week and perhaps I shouldn't have been answering questions. We don't know the exact distance between the heatsink and the pci e slot nor the exact measurements of the cards.. The best we can do is find a card we think can fit. Worst case scenario, he has to return the card because it wont fit (I recommend amazon because of effortless and cost less returns). Hopefully, he will let us know if it fits or not so others can use this information.
The best single slot card I can find that isn't ridiculously overpriced is a single slot r7 250 (hd 7750) from xfx. I have found a much smaller, shorter gtx 750 ti that barely protrudes past the end of the pci express slot. For the record, its more than twice as fast as the r7 250. Please, post your results so others can use the information.
r7 250 (fairly certain it will fit):
http://www.amazon.com/XFX-250E-800MHz-Graphics-R7250EZNP4/dp/B00JM5XX9O/ref=sr_1_7?ie=UTF8&qid=1422759024&sr=8-7&keywords=r7+250&pebp=1422759020476&peasin=B00JM5XX9O
gtx 750 ti: http://www.newegg.com/Product/Product.aspx?Item=N82E16814127836&cm_re=gtx_750-_-14-127-836-_-Product