There should be no problem getting oil pump (or any) parts for your 034. As a matter of fact, many parts between the 034 and 360 are interchangeable, if not exactly the same. I believe the oil pump is one of those parts.
If the saw isn't oiling at all, check the filter in the tank and the oil pump drive gear that runs off the clutch. If oil is pouring out from behind the clutch, but not making it too the bar, then it could be as simple as the oil line being cut or broken. It is common on these saws for the clutch bearings to wear and then the clutch cuts into the oil line.
If the saw has had a lot of use, the oil pump internal clearances will become too great and it won't pump anywhere but out from behind the oil pump gear. The pump will need replaced at this point.
Those are great saws and worth putting a few $$ in to get them running right. I just went through my 034S and replaced the whole oiling system. It was well under $100 for the pump, inlet hose, filter and drive gear. No problems getting it.