Regarding the IHKA (you referred to it as the CCU)...was it a new or used unit...and did you have the IHKA coded (especially if the part number was different or it came from an e39, or if was configured differently than the original (REST or MAX button)?
Although it mentions the e38 in the info below...the e38, e39 & e53 share the same HVAC design architecture (even though the IHKA panels are slightly different)...the underlying operational functions are very similar. Sometimes swapping in a new IHKA will work flawlessly, but if there's anything different...like a different software number...the IHKA will need to be coded. You can also hook up to BMW diagnostics (or some of the aftermarket software) and pull the fault codes from the IHKA. As you can see in the info below...it was designed with an EEPROM to be able to store not only memory but fault codes. So if there's an issue with the IHKA (CCU)...a simple diagnostic check up would highlight any faults.