Sorry to hear that. The digitizer is what converts your finger input into a signal the phone recognizes, so if THAT was broken, you'd see an image on the phone but wouldn't be able to interact with it. Since you say you see cracks underneath the glass but not on the top cover itself (yeii, Gorilla glass!!), then I'd say it's definitely the AMOLED display (Not LCD, remember the S4 uses a different technology). In that case, you need to change the AMOLED screen and, unfortunately, it ain't cheap.
But just for fun, try this. Remove the battery from your device. Put it back in. Now press POWER, the HOME button, and VOLUME UP button at the same time and hold. Does the screen show anything after about 10 seconds? This key combo lets the phone enter "Recovery Mode", so the Android OS is not really kicking in. If the screen comes to life in this mode, it means your screen is alive but the software, after it boots, is not recognizing. If it comes alive, doing a factory reset (which you can do from Recovery Mode) should fix it. If it doesn't show anything, then yeah, your screen is dead.
In any case, since you say you see cracks all over, I'd still get the screen replaced anyway.
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