Paid for adobe illustrator plan and majority of tools are locked

Do you mean that you can see this:

That isn't the toolbar; it is a menu for choosing what items you want in the toolbar. If an item is greyed out, that means it is already in the toolbar somewhere.

In the default basic toolbar, it is under the Rectangle tool, for example:

Click and hold, or right-click, to access stacked tools, or alt-click to cycle through them.

Have you actually created a new document? What are the specs? What is your system? You need to be more specific.

Mylenium