I think that most 775s have push pins...
Depends on what you had previously installed.
The socket 775 hole configuration is standard.
The stock heatsink/fan from Intel will be a clip in (turn screw from the top)(push-pins).
If you ever installed or had installed an alternative heatsink/fan there might be a backing plate on the motherboard. In this case you need to remove the board to replace the heatsink.
No board will have "screw ins". If there is no back plate then there might be threaded offsets standing on the case behind the board.
Anyway if the standard Intel "plug and turn screws (push-pins)" do not work you need to see what is on the back side of the motherboard.
hi