Kernel panic - Mac won't allow me to log in
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...

HTH