i too thought first my mini is rubbish and broken and i was resetting , reinstalling for a whole week trying to get the hp monitor to work on vga , as i first had no dvi cable , but it isnt its these lcd makers who out of their mind put some connectors on their monitors/tv's but forget to programm their devices proper , yes there are little chips inside every monitor nowadays which tell your Mac for example what display is connected when pressing detect display and for the menu to work , so i sold that hp monitor again and bought a acer monitor
another thing i found on that way i bought one of these fancy gold plated dvi cables , it looks the same as the standard one that came with the acer monitor
but has golden connectors (bit of spray paint i suppose ) and i did want a white cable
but when i connect the mini with this cable (looks really exactly the same same pins as the one that came with the monitor i checked several times over and over again if there might be a pin missing ( at the end i even opened up the cable to see if all pins are proper soldered on , they had been soldered on proper)but
my mini is unable to detect the monitor with this cable when you press detect display , it does however display a picture fine and some resolutions but not the original resolution of the monitor ,it displays 1280x 768 but monitor standard is 1280x800 (at least that whats written on the box and manual) with the original cable it displays 1280x800
so check the cable too 😉
because i doubt as much that its your g4 graphics as i trust a politicians word