I have heard of a few 1970 s Oxford coils burning out due to condensation in the cooling oil so I would suspect this with your welder. I would dismantle the welding set, check the oil for water/gunge etc, check the coils with avo or whatever it takes and if they are ok refill with new oil and reassemble. I don't know about the cost of the oil but I recon this is the only way to proceed.
Might be an idea if alls well with the coils to fit a tapping on the bottom of the welder box so future water can be drained off.
Good luck with it, Brian (",).