Ross Tech website is the best source of information for VAG related codes. They are the guys behind the VCDS software.
http://wiki.ross-tech.com/wiki/index.php/16985/P0601/001537
Before spending money on an ECU, check the simple stuff first. Battery condition, charging system operation, ECU supply voltage. Could be something as simple as a corroded terminal. Changing entire wiring looms is overkill, far better to isolate the problem and fix it. If it turns out to be a problem with the ECU itself, you might be be able to update the software rather than replace the entire unit.