The water is heated in a zinc-aluminum alloy cast chamber. The alloy (aka Zamac, pot metal, etc.) is ubiquitous, but not metallurgicaly stable. A fraction of them warp or crack in months or years and others may last 6 or 7 decades.
The manufacturer's description of the water heater in this machine is "boiler" part number MS-0050944. It appears to be available in North America for around $65.
The remaining $165 for the $230 repair estimate would be for installing it and any parts that were needed you didn't mention and for testing it to be sure it worked properly.
The answer to the "answer" that was actually asking about using duct tape ... No, not on the outer case, that just traps the water somewhere it doesn't belong - and not inside, because even if it works to fix something like a cold water tank, it isn't food safe so putting it in your morning coffee puts your health at risk.
Oliver Street, August 2015
