Okay, place cubemaps everywhere you possibly could. Keep aware that each cubemap will increase filesize, but the game uses these to build your reflections (what the checkerboards are currently standing in for). Try to put one in every room/major combat area, so that the reflections on weapons/floor/etc. look right. Also place them at 64 units above the ground to emulate a player's eye level.
Make the cubemap size the default (32). Your cubemaps are too big for your screen resolution; it's impossible for the game to build them because they are so large. The default cubemap size will be fine.
Ingame, type in the console (~ key):
mat_specular 0
buildcubemaps
mat_specular 1
disconnect
sv_cheats 1
mat_reloadallmaterials
sv_cheats 0
Then load up your map and the checkerboards will be gone.