Hi mad380se!!!
First of all, Weldcome to the forum!!!

If everything is like you describe, then it's definitely somewhere in the High requency circuit... Like Dave mentioned, it's more than likely the HF capacitor that's shot but, make sure the HF transformer is working properly before one assumes that it's the capacitor... Most important is to have someone that is competent in troubleshooting electro- mechanical & electronic components because, if the person diagnosing the components doesn't follow the schematics properly when testing under a load, that person is sure gonna get zapped!!! In other words, if you do not know how to troubleshoot components with electricity going through it - for heavens' sake, leave it to someone that does!!! Let us know how you make out, and all the best to you. Oh I almost forgot, make sure the spark gap is correct according to factory specs, nad check hte surface of the gap electrodes to see if there is any pitting because, one might have to also replace the electrodes in order to get optimal HF output.

Respectfully,
Henry

You should see an intense blue sparking at the points where You set the .008" gap. As Henry points out You need to check the rest of the HF circutry as well, and it operates at extremely high voltage, so it is not a job to be taken lightly. The capacitors are not cheap, I am trying to locate a direct source for them, I think I have determined the manufacturer but havn't tried to buy any directly yet. If anybody has a source other than Miller, I would like to know.

Well, for your other unanswered question:
No, you should not be able to scratch start on A/C with a sinewave machine.  I do not know if that is possible even with a conventional squarewave machine, but it would be possible with a good inverter squarewave machine (the waveform needs to be -really- "square" for the arc to be maintained past the zero crossing).  I know my Dynasty supports lift-arc for A/C, and the HF isn't continuous either.

All great advice.  I don't want to step on anyone here, and this probably won't help, but:

Could there be anything conductive between the the points (gook, dust, or worst of all grinding dust containing metal whiskers).  At the voltages of the HF, just about anything is conductive (even AIR, because this needs to produce an arc to jump through it).  Just one tiny whisker of grinding dust (just pass a magnet of the dust near your grinder, and you'll recognize it from the furry friend you just made), could short the points and stop the spark.
So, the gap points need to be clean, and dry.  If they're exposed to the ventilation in your machine (as they are in mine), and not sealed, regular blowing out with air may be required.  If you must, its best to clean them with electrical contact cleaner, or something that leaves no residue, like acetone, but keep the flammability issue in mind with something that is supposed to spark.  :)
There are a number of other places that the HF could be lost to ground, but if you're not seeing a spark between the gap points (in a dim room), then the problem is somewhere within the HF circuitry.  Now, when you say you hear noise . . .  I've always associated something between a buzzing and ticking, as coming directly from the spark in the gap.  The arcing sound is pretty distinctive (these are microscopic sized thunderbolts afterall), and if you're hearing it, but not seeing a spark at the gap, then it could be arcing elsewhere (not good). 

Dave:
My company deals in electronics.  I you can get me a part number for the capacitor, I should be able to get a datasheet, and cross reference a replacement.  Maybe even source something.