I think the vac pump is there to supply vacuum to stuff like the door locks when the engine is off. Take the title to the dealer and get yourself some new keys. I never hear the pump running either but that may just be because it's quiet. Take the rear seat bench out and use the key on the driver's door or trunk and see if you can hear it run. However, since you only have the valet key that might be the trouble right there.

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'02 BMW 325i
'85 300D 450k
'93 190E 2.6 170k(killed by tree)
'08 Ducati Hypermotard 1100S 6k
'06 Ducati S2R800 14k(sold)