Hp prodesk 400 g1 : >5 yrs old , original PSU is only 300w
When you upgraded PSU, what did you install? 600w is good size for GTX 960.
I am assuming that you have confirmed good operation of monitor and cables on another system.
problem: no display on monitor
1. confirm monitor has power (blue or red LED lower right of bezel) and the "brightness" setting is turned up
2. remove connection at monitor end of cable and reattach
3. remove connection at card and remove card
4. inspect card closely under strong light - look for burned elements
5. test gpu on another system
Since system is older, consider thorough cleaning and replacing thermal paste.
Similar, but more thorough advice is available here:
https://www.computerhope.com/issues/ch000241.htm