Oct 29, 2014 05:25 AM|Zhi Lv - MSFT|LINK
According to your description, if you want to make the button visible or invisible, you could set the visible property on button click event.
For the 404 error, I suppose the reason is that the page cannot be found. So, please check the URL.
Here is a sample about Show/Hide Web Controls in RadAjaxPanel, you could reference to it.
And, for more information about 404 error, you could refer to the following link.