The more of the symptoms and odd behaviour we get helps narrow the issue down further. I'm almost certain the BSI is the cause. But in order to get it fixed, you would need access to Lexia in order to take a note of all the ECUs and parameters that are there to compare against and telecode back in once you had the BSI back, after it had been programmed and coded to the car, which a dealer would need to download for you. So possibly a £150 to repair the BSI and say another £100 - £150 ish for the dealer to programme the BSI.
Remote diagnostics are not the easiest thing to do!

If you are gong to move it on, you might want to put a post up in the For Sale / Wanted section here:
viewforum.php?f=7
Best of luck.