[T-Mobile Samsung Galaxy S 4] Biker1:
Don't panic. Your S4 turns on, and you see the logo but it freezes. That's ok. You have a soft brick, and that is able to be fixed without issue.

Please read the general stuff below so you have an idea about what the procedure will be to get back to Stock. After you get back to stock, and your S4 is as it was when you first got it, you can always Root again if you wish to, or leave your S4 stock. It is up to you.

Make sure you have juice in your battery, at least 50%.

Pull the battery, wait 30 seconds, and reinstall it, but Don't power the phone up.

Press the Power button and Volume down button at the same time to get into download/ODIN mode.

If the above is successful, you will be able to Unroot your device and return it to bone stock. You can pull the battery again to get out of download mode, read the basics and links below to prepare for returning your S4 to stock, and once you do, you can enter download mode again and begin.

Charge your S4 while you're reading and downloading the necessary software.

Here are the basic steps to do this.

I've enclosed links to tutorials. Take your time, and don't panic. You'll get back to stock in no time, and the store will never know you were Rooted ;)

Flash the Samsung Stock Firmware. You can find the link here:

http://xdaforums.com/showthread.php?t=2267895

You want to download the stock image to your pc and install it on to your S4 via ODIN.

To get into ODIN mode on your S4, pull the battery, reinstall it, but leave your phone Off.

Press Power and Volume down buttons at the same time and hold them till you see the download screen. Then press Volume up.

Before you install the stock image, you want to download Triangle Away from the Market, and Reset your counter. You can only do this when you are Rooted.

You can see it says Custom when you put your S4 in download mode as per the instructions above. You want that description to change from Custom to Normal (I forgot what it changes to, but you'll see it after you check it again after installing Triangle Away.) Follow the TA instructions carefully, and don't rush.

Since you can't install or get to Triangle Away at the moment because your device can only get into ODIN mode, you'll need to flash the Stock Firmware, Root, install and use Triangle Away, then Unroot again.

Before doing the above, if you can get into your custom recovery, flash your Nandroid (Backup)

I didn't mention this before because you said you couldn't get into Recovery, But you also said Download mode 'doesn't do much,' which is unclear as to what exactly that means. So just check if you can get the S4 into Recovery mode.

Pull battery, reinstall, Power and Volume UP buttons at same time. Hold until you see Logo and blue letting on upper left corner and release buttons immediately.

The above are the basics, and things you need to do Before you Unroot but you can find specifics in the threads here under Unrooting your S4, etc.

After you Unroot, go to Download mode again and check that the descriptions are all changed from Custom.

Check your Device Settings and make sure About device in Status is changed from Custom. And check the settings that you now display the stock Firmware, etc.

This will help you out:

http://xdaforums.com/showthread.php?t=2335109