My aunt's iPhone 4 was jailbroken the day it was bought. And about last month, she updated it. Suddenly the screen went blank only the apple logo was showing. She can't fix it with iTunes because she forgot her account. Is there any way to fix this without iTunes?
You can try to restore it without the help of iTunes. Make sure you have the latest firmware, which you can download from here.
Then download the latest stable release of redsnow here
You can follow the tutorial here on how to restore you iPhone to the latest firmware. Please note that this will erase all your files in your device, which includes the jailbreak. Hope that helps.
You can try to put your iPhone into Recovery mode:
1)Plug the device's USB cable into your computer only.
2)Hold down the device's Home button as you connect the USB cable to it.
3)When you see the Connect to iTunes screen, release the Home button. If you don't see this screen, try steps 1 through 3 one more time.
If that doesn't work, you can try the method like using FonePaw iPhone Data Recovery because it works not bad on this issue: How to fix iPhone stuck on Apple logo?