This article is concerned with the optimal control problem for the linear stochastic system X(t) = x + integral(0)(t)(A(s)X(s) + B(s)u(s) + f(s)) ds + integral(0)(t) Sigma(i=1)(d) [C(i)(s)X(s) + D(i)(s)u(s) + g(i)(s)]dw(i)(s) with the convex risk functional J(u) = EM(X(T)) + E integral(0)(T) G(t, X(t), u(t))dt. In order to guarantee the existence of an optimal control without any(weak) compactness assumption on the admissible control set, we assume that the risk function M is coercive and that Sigma(i=1)(d) D(i)* D(i) is uniformly positive, rather than to assume like in the control literature that the running risk function G is coercive with respect to the control variable. In this new setting, the running risk function G maybe independent of the control variable, and therefore the so-called singular linear-quadratic (LQ) stochastic control problem is included. A rigorous theory is developed for the general stochastic LQ problem with random coefficients, and the bounded mean oscillation-martingale theory is used to account for the concerned integrability. It plays a crucial role in the following exposition: ( a) to connect the stochastic LQ problem to two associated backward stochastic differential equations (BSDEs) - one is an n x n symmetric matrix-valued nonlinear Riccati BSDE and the other is an n-dimensional linear BSDE with unbounded coefficients; (b) to show that the latter BSDE has an adapted solution pair of the suitably necessary regularity. This seems to be the first application in a stochastic LQ theory of the BMO-martingale theory, which roots in harmonic analysis. Furthermore, with the help of an a priori estimate on the risk functional, existence and uniqueness of the solutions of backward stochastic Riccati differential equations (BSRDEs) in the singular case is reduced to the regular case via a perturbation method, and then a new existence and uniqueness result on BSRDEs is obtained for the singular case.