My MacBook Pro is going through some sort of kernel panic, however it is not letting me log in at all. It just keeps restarting and playing the chime music before showing some error code text on the loading screen. Then the cycle repeats. Is there any way to fix this?
Something like that happened to me after upgrading to El Capitan. The system would only behave "normally" if I started it in safe-mode (https://support.apple.com/en-us/HT201262)
So I tried restarting it again in verbose mode (https://support.apple.com/en-us/HT201573) and just before the "panic" message, there was a reference to a kernel extension (kext) for a very old program that I didn't even remembered installing...
I fixed it by restarting the system again in safe-mode and unloading that kext. The next boot, the system began again working ok...
I would follow the sound advice given by Gio. Specifically, boot holding down the COMMAND KEY ( has the apple icon ) and V, to boot in verbose mode. Then let the boot up fail where it might, and reboot in safe mode by holding down the SHIFT KEY.
Proceed by logging in, and then examine the startup logs — depending on your command line skills or lack thereof — via Terminal or the Console app which reside in /Applications/Utilities. You might start with /var/log/system.log.
As Gio correctly stated — often the trouble at boot up is caused by a kernel extension loading or the lack thereof.
Let us know if you are able to boot in safe mode, and what you find in the logs.