This paper presents the effects of laser radiation, non-uniform electric field and roughness of the rigid boundary on Rayleigh-Taylor Instability (RTI) at an ablative surface of a thin target shell of Inertial Fusion Energy (IFE) using linear stability analysis. We consider an incompressible poorly electrically conducting plasma bounded below by a rigid rough surface and above by an ablative surface. The growth rate of RTI including the effect of radiation is derived which is analogues to the form given by Takabe et. al. (1985) for compressible fluids and that given by Rudraiah (2003) for incompressible fluids with nano-structured porous lining. It is shown that the electric field and the roughness greatly reduce the growth rate compared to that in the absence of both electric field and roughness. The cutoff and maximum wave numbers and the maximum frequency are obtained. The ratios of growth rates are numerically computed and the values are tabulated for different values of roughness parameter, electric number and bond number. The results are tabulated. We find that the combined effect of electric field and roughness reduces the growth rate of RTI considerably compared to the classical growth rate.