Well, FWIW 1080 i is interlaced and 1080 p is progressive scan, differences being explained more exhaustively
here
seems that the LG is interpreting the PC input via HDMI as a HD image as from DVD player, Blu Ray etc. The DVI appears to be interpreted (correctly) as a PC image input.
That's my guess.
The features for your LG show that it has 3 picture modes to choose from. Have you tried changing the mode, or is that just for Video image (like "cool, warm, personal etc.")?