I can only play Minecraft in an Administrator profile?

Whenever I want to play Minecraft I have to 'run as administrator' for it to work. If I don't do this, it loads the launcher, but then when I click 'play' I see the Mojang logo in the small window, and then the entire window greys out, and says it is not responding?!

What do I need to do to get it to run normally, without being an admin.

I think this is also having knock on effects, such as the fact my resource packs do not show up in game, even though they are installed on my computer in the correct way. They are all up to date.

From you saying that you see the Mojang logo and the window greying out, I think that it might be just that you have to wait or something. Otherwise:

You could try deleting your.minecraft folder from your %appdata% (make sure you backup your ".minecraft/saves" before doing this!) and redoing the download of minecraft. It could be to do with your resource packs or something.

You could also trying updating your Java, as it could be old (Make sure it is Oracle Java not OpenJDK!).