What an owner does to his own stuff is far different to what a welding shop would do. A reputable welding shop would not touch it. They do not want a call back on an iffy job like this one. 30 years old? Even at 15 years it has outlived its economic life. I seriously doubt the it withstands 2000 PSI steam. You are talking superheated steam, you would not see the steam coming out of the leak. I would be surprised that tubing is schd 80, looks more like a lot thinner tubing. Sched 80 will not withstand 2000 PSI.
Welding; I doubt you can get it clean enough to TIG it. I would opt for an O/A welder with a #0 or #1 tip. Thin tube then go down to a #00 if I was going to try it.
What was it used for? Hot water/steam cleaner? Time to buy a new one, or get the replacement coil, and hope for the best on the other components. What would a whole new system cost compared to fixing?
You have an economic decision to make.
Ron