I can't find a listing for a 034115109 oil pump. I did find images of one and it looks a bit like a 3B oil pump (you didn't say which engine you have).
"The oil pump is driven off a washer on the nose of the crankshaft (Item 2, PN 034105177 below). The oil pump is a gear pump which means the oil pressure is created by two rotating gear wheels as their teeth intermesh, causing pressure as the grear teeth try to compress the mostly incompressible fluid (the engine oil). If the pressure gets too high for some reason in the pump, the pressure pushes against the pressure release piston and spring, releasing pressurized oil back into the oil pan. Note: The ADU in the RS2 originally used the 054115105D oil pump from the AAR 10V five cylinder gasoline engine instead of the more common 054115105E that the AAN and ABY use. However, the 054115105D was dropped on Jan.11, 2002 in favour of the AAN/ABY oil pump (the 054115105E). The 3B (and NM and 7A) use a 034115105B oil pump."
REFERENCE: http://forums.quattroworld.com/s4s6/msgs/93029.phtml
3B 034115105B oil pump:

The "Cap" on the oil pick-up should not be inverted. Sounds like yours is getting sucked into the pick-up tube, blocking oil flow to the pump

Check the strainer under the cap for debris if you haven't already
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