sorry its my first post, but trying to help out the family mini

Model: ONE
Year:2003
Description of problem : The engine managment light has come on on my sisters car (above spec)
Every morning/time started, it takes two turns of the key to start and runs in limp mode
we've taken it to a specialist who has scanned the OBC and said its one of 3 things...
before we throw £100s at it to get it rectified, i was hoping that someone on here has had the same
symptoms, and knows how to rectify it straight away, without going through the process of elimination
Any non-standard parts that might be involved with the problem? just a stainless backbox fitted 2 years ago