In this paper, the capacity region of the diagonal vector Gaussian finite-state multiple access channel (MAC) with partially cooperative encoders is derived. The diagonal vector channel models an OFDM based communication system. Partial cooperation here is in the sense that the encoders communicate with each other through finite-capacity links. The channel states are assumed to be governed by a Markov processes. Full channel state information (CSI) is assumed at the receiver, while only delayed CSI is available at transmitters. The capacity region is presented in a convex optimization form, thus it can be easily computed using numerical tools. The region is derived by first upper bounding the general capacity expressions and then achieving these upper bounds by choosing a specific distribution for the channel input vectors. In order to do so, extensions to the multivariate case of tools and properties used in  for the non time-varying, scalar model, are presented.