Common issue. The only way to tell if it's the adapter or the DC-In Board at fault is to swap adapters. If two adapters are the same, the DC-In board is at fault, and requires replacement. Thankfully, this kind of repair is fairly inexpensive as the board itself is a cheap part.
Mac mini (Mid 2011) 2.7 GHz i7, 8GB RAM, Crucial M4 256GB SSD + 500GB + 1TB FW800 OWC Mercury Elite Pro mini
iPhone 4S • iPod nano 8GB • Sound System Audio Engine A2 • Display UltraSharp U2412M 24"