I see this is your first post. Welcome!
Firstly, welders involve high voltage that can kill you. If you are not qualified to work on such equipment, stop and seek professional help. I assume no liability for any risk that you take.
For example, discharging caps... particularly high voltage caps, like what might be in a welder, with a screwdriver is bad and dangerous practice. It can weaken and damage the cap. It can arch and throw molten metal into your eye, etc. Yes, discharging the caps, before working on any electronic device is essential. But, you need a proper discharging tool to do that. They can be made easily with a bit of wire and high value/wattage resistors. But, you need to acquire that tool, before continuing.
With the liability stuff out of the way, let's see if we can get you better positioned to get the help you need. Firstly, you have taken a general and casual approach to writing your post. Therefore, the best that you can expect is general and casual answers. And, this forum tends to deal in specifics. Meaning, your post will more likely be passed over.
So, let's get some details and give purpose to your path... Firstly, we need to know about you... Your electronics knowledge and skills levels. What tools and resources you have, or can get access to. Details about your multimeter, soldering iron, oscilloscope, etc.
You have obviously done some tinkering around and visual inspection. That's a good place to start. But, as that didn't reveal any easy fix, you might want to formalize your approach...
- Start by replacing the known bad Tantalum cap. A simple cheap component can shut down the whole system. It needs to be repaired, before troubleshooting further, because it may be effecting things downstream.
- Divide and conquer... Break the device into parts and isolate the failure. My guess is that the high voltage welding side is okay and that the issue is with the control side.
- Once the failure is isolated to a zone, start with the basics... Verify the various power supplies. Start where the power enters from the wall and follow it out to the low voltage regulators.
- Take lots of written notes, as to in what order you did things, how you did the test and the results. Of particular importance is the exact symptoms you are seeing. No fan, no LEDs, but, if the welder is a wire-type, will the wire advance? Report that back to us.
- With that information, we will continue to divide and conquer, breaking the circuit down and eliminating possibilities. Eventually, we will hit the jackpot.
I hope that helps. My true intention is to get you the help you need. I do not mean to seem as if I am talking down to you. We just need some information. I look forward to working on this project with you.