Okay, I'm not sure if you can do this without Premium... These are the best options I can find.
This prevents guests from seeing the links in your Main Menu. Members can still see/use them. However, if they know the address of it, they can still get to the page..:
-Again, go to your Admin Panel/ Menu. Go to "Edit Menu", which is under the Content category. For each of your pages, click the edit icon. You can then allow only members to use your main menu.
This prevents them from using the panels, such as the chat box:
- Go to Panel Layouts. Hitting the edit icon on the individual panel allows you to choose who can view/use the panel.
For the forums, you have to edit each individual forum board:
- Again, go to the Admin Panel/Menu, then go to "Forum Boards". Click the edit icon on the individual board/topic, such as "General Discussion". If you scroll to the bottom, there are permissions like "Read Permissions", "New topic permissions", etc. And you can check the member box to allow members only.
For the Store page, I'm not really sure if this works. This one is harder for me to test out.
If you go to the "Shopping & Fees" section, then you might be able to edit individual items to allow only members to view that item. I don't have any items in my own, so I can't be fully certain that that is how it works. But I'm guessing you edit each item just like on the edit menu. And mid-way down, there's the Ranks option.
For the other pages, I am not sure how to make those private. When I get time later on, I'll try to find a way to make those accessible to members only. I'm sorry that these are not perfect solutions, but I hope they're better than nothing.