Hi,
as per Kevin`s suggestion, I am posting initialization log (mixed one) from initialization of the GeodeLX board. As it could be clearly seen from the log, VGA option ROM was never called and executed during the initialization sequence, therefore issue with a lack of video output during SeaBIOS stage on this board looks somehow logical. [1] suggests that the problem existed long before, as most users of these boards are Alix owners who do not care about existence of the video output :)
[1]. https://www.coreboot.org/pipermail/seabios/2012-February/003186.html