The skybox is included with the game, so it's probably being overridden by another addon. Try opening the console using Shift+Esc and then entering the following commands, one at a time:

whereis materials/skybox/sky_day02_03_hdrup.vmt
whereis materials/skybox/sky_day02_03_hdrup.vtf
whereis materials/skybox/sky_day02_03up.vtf

The console should show a path and filename in green text each time. If that path doesn't contain the name hl2_misc.vpk or hl2_textures.vpk and instead contains the name of an addon, you need to disable that addon and then restart the game. If that doesn't work, temporarily disable all other addons, restart again and see if it works then. If it does, you can re-enable them in small groups to find out which one caused it.