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For the main topic can a gigayte gtx 960 gpu fit in t3500?
according to many videos on Youtube it can.
whatch this its in Portuguese but don't really need to know Portuguese to understand it works.
https://www.youtube.com/watch?v=KUawZ0zccQo
DELL T3500 Precision - GTX 970 PNY - xeon W3690 Hexa Core - DELL T3500 - 8GB WINDOWS 10 PRO 64 BITS
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I have run a GTX 950 in a T3500. (Close but not exactly your card.)
Looking in the case, most large video cards fit.
Search for images with "T3500 motherboard case" Remember that this is a BTX case, so the metal thing with 2 hard drives on it swings out of the way. See if you think it will fit.
Here is a pic of a very large video card in a T3500. Maybe you can measure the lengths of DIMMs and expansion slots to calculate the maximum card length it can take? https://linustechtips.com/main/uploads/monthly_2017_07/gpub.jpg.0fd60a6283dd62b7fb0ff7eb0890443b.jpg
Sadly, the service manual does not give a measurement.