you need to cut the power swicht cable and make the jumper loop to power up normally, just recently replace my DELL Case to a Corsair 300r and did jumper mod
http://s1053.photobucket.com/user/korros1on/media/Mobile%20Uploads/IMG_20160211_201138897_zpsvgo6j3fp.jpg.html
here is my dell 3847 with a case swap, its a standar Micro ATX,
http://i1053.photobucket.com/albums/s476/korros1on/Mobile%20Uploads/IMG_20160211_203847029_zpsscnlbpnn.jpg
i was having the same issue so i replace my Dell Case, with a corsair 300r
http://s1053.photobucket.com/user/korros1on/media/Mobile%20Uploads/IMG_20160211_203847029_zpsscnlbpnn.jpg.html
you need to cut the power swicht cable and make the jumper loop to power up normally, just recently replace my DELL Case to a Corsair 300r and did jumper mod
https://plus.google.com/u/0/112436299016438504432/posts/LH5UWbFydoG?pid=6250121641750064066&oid=112436299016438504432
i replace mi DELL Case to a Corsair 300r due the heat was generating the GPU, the motherboard is a standart ATX the only thing that you will need to mod its the power button cable to power up.
i am at work now later can i post a pic.
i recomend you this card very low profile
EVGA 02G-P4-3753-KR GeForce GTX 750 Ti Superclocked 2GB 128-Bit GDDR5 PCI Express 3.0 Video Card
NVIDIA GTX 750 Ti
640 CUDA Cores
1176 MHz Base Clock
1255 MHz Boost Clock
Memory
2048 MB, 128 bit GDDR5
5400 MHz (effective)
86.4 GB/s Memory...