Surface thinking wonders if excessive current burnt up a component? It's easy to let a welding rod solidify to the work. We must act fast to prevent ruin. Because even though wise design normally puts circuit protection in place, the tendency is to minimize components in the welding loop since any extra resistance wastes power.
If you think the power supply is still good then I guess you want to build a substitute oscillating circuit to apply to the 4 igbt half-bridge.
Do you have a schematic for your unit? Can you locate a generic schematic for electronic welders?