Solvent-free polymer electrolytes were made consisting of Li+ and pyrrolidinium salts of trifluoromethanesulfonimide added to a series of hyperbranched poly(ethylene oxide)s (PEO). The polymers were connected by triazine linkages and cross-linked by a sol-gel process to provide mechanical strength. These electrolytes are more conductive than those made with high molecular weight PEO imbibed with ionic liquids at ambient temperatures, due to the amorphous nature of the polymer. The connecting PEO groups were varied to help understand the effects of polymer structure on electrolyte conductivity in the presence of ionic liquids. Polymers were also made that contain poly(dimethylsiloxane) groups, which provide increased flexibility without interacting with lithium ions. When large amounts of ionic liquid are added, there is little dependence of conductivity on the polymer structure. However, when smaller amounts of ionic liquid are added, the inherent conductivity of the polymer becomes a factor.