If that is a bare-bones stock game doing that, it sounds like you have a disk version, and neglected to install the DirectX v9.0c and Codecs -OR- you need to change the SH4.exe "Properties" settings (maybe both DirectX and Properties??) by navigating into the game folder, find the SH4.exe file, right-click on it, and then left-click on the "Properties" entry at the bottom of the context menu. That will open the "Properties" settings window, of course, and you will have to experiment with the settings there, as found in this Win10 screen grab:
from a couple of pages before this.
A couple of notes: First, if you plan on modding the game, do not install it in the default location, which would be a "Program Files" folder. You want to make your own install folder, and put it in there instead. That way, Windows (usually) will not interfere with any mods that you add to the game. Secondly, anytime you make changes to the mod configuration, you usually will have to empty the Save folder, which under normal circumstances is "C:\Users \UserName \Documents \SH4", unless you have used MultiSH4 and changed it. As for the DirectX files, you do need to install DirectX v9 files, since those files are missing in all the versions since. Nothing is overwritten by them, they just add to the dll collection. If you use a Steam or Ubisoft download, those usually automatically install those files. Once in the game, you want to match the Graphic Settings to what the "(recommended)" setting in Windows is, since that is your display's "Native" resolution...