What are the symptoms? Does it start up when turned on? Is there a
power light? Do gauges move? Is there a contactor inside? What
controls it?

There are no gauges or lights, and I'm pretty sure there are no
electrically-operated contactors inside.

If I were you, I would boldly open the case and start following the
symptoms and connections with a multimeter. You can, most likely,
figure out just what is wrong by using logic, asking pointed questions
in this newsgroup and beinf meticulous.

The reason I asked here first is because the machine is really heavy
(maybe 250 lbs) and full of oil. Opening it is therefore not an
attractive proposition, and it means that my welder will be out of
service while I'm trying to fix it. I just thought that perhaps someone
could offer some guidance first?

Chris