I'd always do the simple and easy testing, before hanging on parts. First do a static and running test on the battery, to make sure those readings are somewhere around 12.5/13.5 volts. Then remove the TCM connector and examine both sides for corrosion or other issues, and check the wiring going into the connector as well. Reconnect the TCM and see if anything changed. If not, then disconnect the battery, touch the battery connectors together to drain the caps, and then reconnect and see if the problem goes away (even for only a short time).
2011 3i 2.0 A/T 145K miles