How to fix Samsung Note 3 SM-N900 bootloader loop? My Samsung Note 3 SM-N900 got fully discharged and now it's stuck at the samsung logo when I power it back on.

Things that I have tried to fix my mobile:


Wiped the Cache partition from the recovery mode.
Used platform tools for adb recovery, but the device is not recognized in the PC probably because USB debugging was not on.
Soft reset using Home and power button.
Fully recharged the mobile, changed the battery as well. 


I have a lot of important data which I don't want to erase. The last option left with me is to factory reset my device which would result in data loss. Is there any other way to fix the device without losing the data?
You have two ways of recovering you data:


Boot into fastboot and try to flash custom recovery (like TWRP). It allows making partition backups, which you can open on PC later.

fastboot flash recovery recovery.img

Try to boot into temporary custom recovery and do the same (full partition backup). However, this depends on device and can be not available for Samsung Note.

Check this and this tutorial.


What concerns fixing the tablet in general from bootloop, it depends on what you've done/what have happened, and probably cannot be achieved without loosing your data. To be on the safe side, it's always preferable to do the backup prior to any manipulations.