  We consider the following quasi-linear parabolic system of backward partial
differential equations on a Banach space $E$: $(\partial_t+L)u+f(\cdot,\cdot,u,
A^{1/2}\nabla u)=0$ on $[0,T]\times E,\qquad u_T=\phi$, where $L$ is a possibly
degenerate second order differential operator with merely measurable
coefficients. We solve this system in the framework of generalized Dirichlet
forms and employ the stochastic calculus associated to the Markov process with
generator $L$ to obtain a probabilistic representation of the solution $u$ by
solving the corresponding backward stochastic differential equation. The
solution satisfies the corresponding mild equation which is equivalent to being
a generalized solution of the PDE. A further main result is the generalization
of the martingale representation theorem in infinite dimension using the
stochastic calculus associated to the generalized Dirichlet form given by $L$.
The nonlinear term $f$ satisfies a monotonicity condition with respect to $u$
and a Lipschitz condition with respect to $\nabla u$.
