Let's try to use a private browser to check if this is a browser-related issue.
Google Chrome: press Ctrl + Shift + N
Mozilla Firefox: press Ctrl + Shift + P
Internet Explorer: press Ctrl + Shift + P
Safari: press Command + Shift + N
If you're able to add your customer via the private window, go back to the main browser and clear its cache to start with a clean slate. You can also use a different browser.
If you're still unable to add you customer through the customer box, let's add the customer with these steps:
Click Sales on the left pane.
Select Customers.
Hit New customer located in the upper right corner.