Hi,
this could be tricky if you've no experince of faulting to component level.
Basically switch off and remove the mains plug from socket, pop the lid off the welder and sytematically check for loose connections, burning on the circuit boards, etc. If you remove any plugs internally mark them so you can get them back on the right sockets and the right way around.
Maybe do a quick sketch or take digital photos as you're working, etc.
If it is a variable resistor then it may just be dirty, there's cleaning spray that you can buy for a few quid a can from electronics shops...spray inside the resistor and work the control knob left and right to clean the tracks.
If it doesn't work after this and there's nothing obviously wrong then you're down to faulting with a meter.
The variable resistor probably has writing on it stating what it is and if you can get one they're generally easy to change with a soldering iron.
Final option is to find someone who can repair it...look in the plasma cutter folder, someone today posted a company name where they work and said they can repair a Cut40. The Berlan should be similar technology even if it's a welder rather than a cutter and they may be able to help.
Note, there's probably some big capacitors inside the welder, usually look like a small bean-tin...they'll hold a charge for some time after the power's removed so keep fingers away from contacts!
Regards
Peter