Hello everyone. Please read my previous posting and if you have the same issue with your 740iL, I was able to find the problem. It took almost 2 months - the BMW dealers I visited could not figure out what was wrong, as the code did NOT show up (and you know how it is - no code "no problem"). I finally saw a Russian mechanic - during his immigration journey, he worked as a mechanic in Germany and now owns his service center for the past 30 years in US. When he saw my car, he said:
"Don wory - I fix". He said that the scraping noise was 100% NOT transmission, took the computer, connected to the socket under the navigation and started driving my car with the computer in his hand. 10 minutes later he came back smiling "I tell you I fix it - it's yur ABS pompa, when I drive, it's give me code". Who would have thought that a Russian mechanic, who barely speaks English, would have more knowledge and experience that 3 or 4 BMW certified delerships. After he looked up the code, it turned out that the ABS pompa is actually called DSC Compressor (Dynamic Stability Control Compressor) and the part number (for 2001 740iL) is 34516781435. The BMW dealer wanted $854.29 for this part new, I was able to find it used on the ebay for $107 + shipping. Problem SOLVED.
The other funny thing is that I never changed transmission oil and at 160,000 miles asked this Russian mechanic if it is true that you should not change oil, because, as many of you know, the BMW in USA tells you that you do not need to change it. The Russian mechanic (Alex) told me that the BMW person who tell me that, needs to be sent to Siberia. In Europe, the transmission fluid is changed on BMW cars every 30,000 miles, Alex said and "in Amerika zey wont to change transmishan for 5000 dolars, not yur oil for $250". What an experience. So, the moral of the story - if you have the same issue as I described, it is most likely the DSC compressor, and if you never changed your trans fluid - go ahead and do that and replace the filter too. Oh, by the way, do not listed to those who say that your car will not drive after you change it - anothe bunch of garbage ...
Hope I was able to help someone out there.