Can you upload a pic of your optiplex? How do you know it is DT and not MT? It is hard to make suggestions on new graphics card without knowing the model for sure. If it is MT, easier to get a full height card. What is purpose of upgrade? For better resolution or light gaming? Core 2 duo cpu in 780 E7600 will severely limit gaming capabilities. 780 cpu can be upgraded to core 2 quad although the investment worth is dubious in 2020. If it is DT which seems strange given reported spec, more limited in graphic card form factor.
You have a 780 MT. see p.3/40.
https://www.dell.com/downloads/global/products/optix/en/optiplex_780_tech_guidebook_en.pdf Any full height graphics card that has TDP up to 75w and does not require a power connector and length up to 7.4” will do. Most modern graphics card will be bottlenecked by the slow core2 duo cpu during gaming. What resolution is your monitor that you want the graphics card to support.
In the screengrabs are a couple of good combos for your 780. By the way, a Q9650 runs at almost and around $50 on ebay. A Q9550 is almost cheap as dirt. A Q6700 is cheaper than dirt. I'd be tempted to go with the Q9550 2.83GHz and not pay $20-$30 more for a Q9650 3.0GHz. The Q9650 obviously went up around $10 since I bought mine a few years ago (previous 755).
Many thanks for your excellent help. I am just about to buy a Nvidia Geforce GT 1030 card but most of them are low profile. Just one or two the full height.
speedstep
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Posted November 14th, 2020 17:00
Your video connector is LFH DMS59
https://en.wikipedia.org/wiki/DMS-59
I would recommend ditching that and getting a regular Full height card Optiplex Tower Single slot PCI-E
https://www.amazon.com/AMD-profile-graphics-bracket-computer/dp/B00N727RGS/
Or
https://www.amazon.com/EVGA-GeForce-Passive-Graphics-01G-P3-1313-KR/dp/B004KABG1I/
better is
https://www.amazon.com/BTO-GeForce-Graphics-Monitor-Support/dp/B08GQ8RD18/
OR
https://www.amazon.com/VisionTek-Radeon-5450-DVI-I-Graphics/dp/B01CN1F1ZM