A generalisation of the Rouse model, able to describe randomly cross-linked polymers, is used to model polymer backbone dynamics and ionic conductivity in poly(ethylene-oxide) (PEO) NaI polymer electrolytes above the glass transition temperature. In these calculations it is assumed that each Na ion forms a permanent cross-link between two oxygen atoms of the PEO backbone. In this way a coupled set of Langevin equations is constructed similar to the Rouse model for linear polymer chains. By calculating the eigenvectors and eigenvalues of the Rouse matrix, the self part of the intermediate scattering function F(k,t) and the frequency dependent ionic conductivity are obtained. We find that under the influence of cross-links, the relaxation times of F(lc,t) increase, indicating a slowing down of structural relaxations. Also, when fitted to a stretched exponent, we observe a decrease of the stretching parameter p. Both observations are in qualitative agreement with the results of neutron spin-echo experiments and molecular dynamics simulations on the ps/ns timescale. Including the breaking of cross-links into our calculations, the ion concentration dependence of the conductivity is calculated and in agreement with experimental observations. These observations suggest that on short timescales, the conductivity is mainly determined by the cooperative motion of the polymer-ion complex. At longer timescales, the ions can diffuse normally through the electrolyte.