Welcome to Android Central! The Downloading screen means you got into Download Mode (which is usually accessed by powering on using the Power, Home, and Vol Down buttons). It's used if want to download a firmware file and install it manually. If you're not actually connected to the computer and actively downloading a file, you can power the phone off, then power on normally.
I'm not sure if you had to buy a new battery. Use either of your batteries, and let the phone charge on a wall outlet for at least 4-6 hours without disturbing it. Then try powering on again.