Have you been through THEBERBSTER's post
SH4 <> TUTORIALS <> HOW TO DO IT <> INFO <> DOWNLOAD LINKS -STICKY INDEX? If you have Windows10, try the ideas for the video drivers. Windows seems to have trouble with every-other update. One will be fine, the next trashes the video and / or audio. THEBERBSTER also has a link to the CapnScurvy LAA in Windows 10 thread.
Do you have Windows set to the "Native" resolution of your monitor also? Does the game still mess up when you choose that same setting in the Options menu of SH4, or is it available as a choice? You could try right-clicking on the SH4.exe file, choose "Properties" from that context menu, then click on the "Compatibility" tab. Try the "High DPI scaling" settings. In Win 7, it's a little tick box that limits scaling, while in Win10, it's a settings dialog that has a little more control over the settings...
If you keep having issues, be sure and post back with your video card (or if it is an onboard, what the chipset you have is), and what the OS is. If it's Windows 10, which build is it? How much RAM do you have?