BMW Repair: main relay staying energized, new bmw, air valve

Question
 John,
97-328i. Main relay right next to fuel pump relay energized all the time. Even with key out. Tried swapping relays. They are light green, but do not fall under bulletin date code. Further, noticed because air valve buzzing so long as relay is installed. This drains batt. Have installed new BMW battery and must unplug main relay at every stop. New batt. has not been allowed to dischage as I discovered problem prior to batt. install. Have driven for several days w/no other symptoms, codes/lights. Shorted idle valve? Short to grd. on DME grd.? DME? Car is clean, hasn't been butchered/abused. Seen/heard anything similiar? Thanks for any thoughts.

Answer
I like your debugging....except not sure what you mean by "not fall under bulletin date code".

I'd stay on the path you were on before that.  Try swapping with another relay.  If there isn't another one in this model, (and you don't have a friend with a 328), it would be worth buying one.

DME grounds, bad DME's, etc. are nasty, and unlikely.  It's usually the simpler items.