How are you referring to other files within the index.html? They should be relative paths, either flat within the same directory like src="spritesheet.png" or in subdirectories like src="images/spritesheet.png", and if they're in subdirectories then the zip file needs to have the same directory shape.
Viewing post in My HTML game don't work
Try using your browser's development console. It varies from browser to browser a little, but it can show you what requests the page is making when you load it and you can see whether it's requesting the files you think it's requesting and whether they're coming back as 404 errors.
In Firefox, you'd open your game's iframe in its own tab, then in that tab press-control-shift-K, then the "Network" tab of the console UI that appears. I think Chrome is similar but with control-shift-J, or possibly some other combination if you happen to be on a Mac.