I guess that the IGBTs are not cheap, so it is important to ensure that the new ones do not get destroyed again.
As a full H-bridge circuit, control and timing of the circuits that trigger the gates of the power transistors is critical.
The left and right "vertical strokes" of the H contain two transistor switches each, one at the top and one at the bottom of each vertical, for a total of four. The primary of the main inverter transformer is the "horizontal bar" of the H. It is a ferrite-cored transformer with a high-current secondary, and typically operates at 20- to 100- kHz. The main 325v DC power bus is applied across the upper and lower "ends" of both verticals of the H.
When a trigger pulse is applied to the gates of the top left and bottom right transistors, current will flow across the transformer primary from left to right. After that pair turns off, the top right and bottom left switches of the H will get triggered on, causing current in the primary to reverse, going from right to left. This makes DC into AC !
Obviously if the gate pulse timing is wrong, or even permanently "on", then the transistors will short the DC supply. The main supply breaker will trip and the transistors will probably be destroyed.
A further difficulty is that the high-impedance gate of an IGBT can pick up any stray voltage or leakage and result in turn-on of the device, full conduction, and self-destruction! Therefore gates must never be left open-circuit or floating, which can happen if a failed transistor is replaced with a new one without first confirming correct functionality of the entire gate control circuit.
To do that, you will have to trace the full gate circuit, test all the components, and verify correct timing. There will be a pulse-width modulated ( PWM ) pulse generator, Zener diodes, series resistors, TVS ( transient voltage suppressors ), current drivers, maybe pulse transformers or optocouplers, etc.
The MIC4422 is just an amplifier and signal inverter, allowing a 10 microAmp input current to drive up to a 9 Amp output.
It is probably quite rugged so unlikely to fail, but may be only a small part of the gate circuit.
One way to confirm that all is OK before risking another set of IGBTs is to replace the 325v DC bus from the AC mains, the input rectifier, and the capacitor bank with a low voltage current-limited DC supply, of about 30 to 40 volts, then check for valid control signals on all the gates with an oscilloscope.
Another option is to fit a set of cheap low-power IGBT devices. That will not allow actual welding to be tested, but all the gate voltages and timing can be verified.
Here is an earlier thread describing the successful repair of an inverter DC TIG welder, and it explains what is involved:
I have an XTT182DV inverter set, which is currently not showing any signs of life.
A preliminary investigation is showing that I am getting AC voltage to the first pair of rectifiers and when the DC side of the rectifiers is disconnected from the main PCB there is 240V DC. When the DC side of the rectifiers is reconnected, the voltage is pulled down, possibly indicating a short circuit.
Since the DC voltage is getting pulled down, there is no voltage on the control side, therefore no power indication light or anything else. Nothing is tripping as the short circuit load is being...
According to Post #32 of this current thread, this Selco service and repair manual also applies to the Lincoln Invertec: