What version of Firefox are you running?
Your password-protected post page looks fine to me in Firefox 31:

Could you please make sure you’re running the latest version of Firefox?
I had changed the theme since I had to take the quiz. You may check it now http://varctest.prepvelvet.com/vt-38/ . This doesn’t work. I’m using firefox 31.
I had another look at http://varctest.prepvelvet.com/vt-38/ and it still looks fine on my end with Firefox 31:

Does it look different on your end?
You might try deactivating all your Firefox extensions to see if something is interfering for your display. Here’s a guide to running Firefox in “safe mode” (without extensions) for troubleshooting purposes:
http://support.mozilla.org/en-US/kb/disable-or-remove-add-ons
Please try to enter the password in the box. You won’t be able to do that. I’v deactivated and activated all the plugins, yet I was unable to type in the password box.I switched the theme and it worked all right.
http://varctest.prepvelvet.com/vt-42/ has another theme where one can enter password easily.
Please try to enter the password in the box. You won’t be able to do that.
Ah, I see what you mean.
I just set up a local test site running WordPress 3.9.2 and Isola 1.0.3 and a password-protected page. I was able to enter the password normally in Firefox 31.
Have you made any changes to the Isola theme files or added any custom CSS? If so, could you try reverting back to the vanilla untouched theme and let me know what happens?
You won’t be able to do that. I’v deactivated and activated all the plugins, yet I was unable to type in the password box.
Just to clarify so I’m certain, did you try to type in the password box while all plugins were deactivated?