Could be the fuel pump and it could also be a charging system problem.
The fuel pumps have had the warranty extended due to melting/overheating of the connection. See this thread -
http://www.xoutpost.com/bmw-sav-foru...mall-leak.html
The fuel pumps are no fun to replace in the E70 compared to earlier BMW's.
Also while I like Carly for some things, you NEED to get OBDFusion. Carly falls WAY short in general OBDII support and Logging. You should be able to use the Carly interface with OBDFusion.
In the short term get the codes read, most auto parts stores do it for free, however, if the SES/CEL/MIL is not on, you may or may not have Pending codes.
Get OBDFusion, you will not regret it. Less than $10.