It appears that both of you (Rondan and petesmc) are dealing with a ground fault condition that is tripping an RCD or GFCI. This is a potentially dangerous situation and can be difficult (maybe even lethal*) to diagnose unless you really know what you are doing. I agree completely with Jake about taking it for professional repair or getting some hands on assistance by someone qualified to to this sort of work.

Rondan wrote:Then, to isolate other problems, I disconnected the other wire from the heating element and wired it directly with an external cable to the wall plug and it started to heat up the water, which means that the heating element is OK (I didn't ground that cable!) and the fuse didn't blowup.

If you have a ground fault and wire it up without a good ground, the machine will work unless something or someone creates a current path to any ground, then it will trip the GFCI or RCD. If the current goes through a person the GFCI might prevent a lethal shock, but not good to rely on that.

Rondan wrote:That's the strange part, I checked it and he doesn't show any measurable resistance or a shortcut, it is as "disconnected".
...
Yes, same results, no shortcut to the ground.

If your multimeter shows conductivity between either terminal and ground, that's a conclusive test that you do have a ground fault. But it doesn't work the other way around: A good test of no continuity on a simple multimeter is no guarantee that you don't have a ground fault. Even a high quality multimeter may not detect all ground fault conditions. There are special tools for that that are designed to test for small current leaks under full voltage.

*On average, about 5 people are killed every year in the US from trying to troubleshoot or repair a small electrical appliance. https://www.cpsc.gov/s3fs-public/Electr ... ctKRABjYDv