usually if it's ticking, everything in the PSU is alright (again, *USUALLY*). The starter circuit uses the same voltage as the tube to convert into a high voltage pulse, so usually ticking means the head is getting the high voltage DC and it's trying to fire.
Does the tube 'flash' at all while the ticking is happening?
I'm not sure about the smaller SP argons, but I know on JDSU argon lasers the current ramps all the way up for the starting of the PSU, so that seems normal to me, but I could be wrong. The reason I would guess that nothing is getting hot is because this current isn't going anywhere yet. It's probably just displaying what it's 'trying' to send to the tube rather than what is actually flowing across it. As soon as the PSU senses voltage across the tube the current instantly drops to idle or whatever it's set to.
Stick a white card directly in front of the output aperture while it's ticking and see if you get any flashes. No flashes while it's ticking either means the tube is up to air, is severely high pressure, or the start pulse is not getting to the tube for whatever reason (shorting to something else?)
If all else fails, pick yourself up a BD-10A hand-held oudin coil from ebay. These are worth their weight in gold. They output from 10-50kV @ ~1mA and are AWESOME for getting those hard-to-start tubes to fire up. It's one of the best laser tools I've ever purchased. One little zap to the tube should cause the argon inside to glow, letting you know there is still gas in there. Then while it's ticking give it another gentle zap and it should fire up. Avoid any seals on the tube and mirrors as the HV arc can poke holes