Broken Arduino Uno, works over USB but cannot take DC in
As you have noticed, measuring voltages is the first step. Here's some voltages for you and what they mean if they aren't there. These are all assuming precisely 12V in through the barrel jack. They are in order of "priority" - start at the top and work down, the first one that fails is your culpret (i.e., the barrel jack feeds VIN through the diode, VIN feeds 5V through the 5V regulator, and 5V feeds 3.3V through the 3.3V regulator).


Roughly 11.4V on VIN - if it's not there the input protection diode has blown
5V on the 5V pin - if it's not there the 5V regulator has blown
3.3V on the 3.3V pin - if it's not there the 3.3V regulator has blown


Fixing it may be as simple as replacing the faulty component identified above - although they are all surface mount and some are more tricky to replace than others.  That said, if it is (as it sounds) the 5V regulator that has gone, that is one of the larger components (SOT-223) so should be eaiser to replace. Also it's dirt cheap - I get them for a few cents each in bulk.