Sers,
I bought myself for 10 euro what I can convert vga to hdmi for ps4 because my screen has no hdmi.
But he gets no signal when plugging in the cable.
These converters usually require a power supply via HDMI because they contain electronics. Your PS4 will probably provide but no power via HDMI with which the converter does not work.
However, if I look at your screen I would rather take HDMI to DVI. These adapters you get for 5Euro and should also work with HDMI devices without this supply voltage.