This study presents a comprehensive Direct Numerical Simulation (DNS) analysis of viscoelastic turbulence in channel flow, focusing on how dilute polymers with high Schmidt numbers (Sc) modify classical energy transfer mechanisms. The addition of polymers introduces nonlinear coupling between momentum and elastic stresses, altering the turbulence cascade by enabling energy exchanges at sub-Kolmogorov scales. As Sc increases, polymer concentration fluctuations become confined to finer scales yet retain a significant influence on the overall turbulence dynamics. Scale-resolved spectral analyses reveal a redistribution of energy from inertial to elastic scales, particularly in the streamwise direction, driven by polymer-induced stresses. Elastic instabilities in the buffer and logarithmic layers amplify turbulence regeneration processes and give rise to non-Kolmogorov scaling behavior in the energy spectrum. These findings demonstrate that traditional turbulence models fail to capture the nonlocal and multiphysics energy interactions characteristic of viscoelastic flows, underscoring the need for advanced subgrid-scale modeling strategies in LES and RANS frameworks to accurately simulate such complex systems.