Failed convergence in PETSc (large non-linear problem)

Hi! My code is too long and complicated to post so I’ll try to describe the problem:
I’m solving a large non-linear system (1 millon dofs to 10), when I try an iterative solver + a preconditioner (most combinations yields the same problem) get the error

Solution failed to converge in 0 iterations (PETSc reason DIVERGED_NANORINF, residual norm ||r|| = 1.387790e-02)

This is in the iteration 1 of newton (the 0 iteration works). What does this mean? I expected a residual = inf becuase the problem is categorized as DIVERGED_NANORINF.
When I try a direct solver the error goes:

*** Error:   Unable to solve linear system using PETSc Krylov solver.
*** Reason:  Solution failed to converge in 0 iterations (PETSc reason DIVERGED_PC_FAILED, residual norm ||r|| = 0.000000e+00).

I’ve read some threads where the advice is to try a custom Newton solver, I didn’t do that yet, I’d like first to know that the problem is not more basic, but I’m aware I should do that.
Can this be related to very restrictive Dirichlet boundary conditions? Too many zeros in the matrices involved? Maybe someone already experienced this kind of problem.

See: Default absolute tolerance and relative tolerance - #4 by nate