We have demonstrated a 104 W multimode, laser-diode-pumped zig-zag slab laser based on conduction-cooling and a novel pumping geometry called edge-pumping. The advantages of the edge-pumped design include efficient pump absorption, conductive-cooling, power scalability, and a simple opto-mechanical laser head design. The multimode laser operates at 104 W with 40% slope efficiency. TEM00 mode operation was demonstrated at 39.5 W for 250 W of pump power with a slope efficiency of 21%. Absorption loss due to the thermally populated lower laser level decreases the slope efficiency at high pump powers. This effect is included in laser oscillator performance models to accurately predict the operation of the oscillator.