A range of low-molecular-weight linear poly(ethylene oxide) chains with LiCF3SO3 have been examined via the transverse proton NMR relaxation. From the measured relaxation functions it is shown that the chains obey Rouse dynamics. This analysis gives the molecular weight of a Rouse statistical subunit and the fundamental Rouse relaxation time. It was found that varying the temperature and salt concentration had no effect on the size of a Rouse statistical segment and therefore none on the conformation of the chains. The temperature dependence of the fundamental Rouse relaxation time was found to be well modeled by the Vogel-Tamman-Fulcher equation. The NMR-measured correlation times were then successfully used to predict the glass transition temperature as measured by DSC. The main conclusion of this paper is that under the addition of salt the ideal glass transition temperature T-0 is found to remain constant or indeed to slightly decrease.