It's possible that a hydraulic cylinder might not fully extend even with sufficient oil pressure if it's mechanically damaged. If the noise is coming from the valve drive, that would suggest the problem lies there.
My car now rattles for almost 10 seconds after a cold start:

But I'm leaving the hydraulics in because I don't want to completely disassemble it.
Remove the valve cover after the engine has been running for a while and then check the valve clearance. If a feeler gauge between 25 and 30 thousandths of an inch fits underneath, the lifter is worn out.
B.Eng (FH) u. KFZ Meister
Seit 06/10: Audi A4 1,9 TDI Avant Quattro mit AVF.
