Odds are if unplugging and plugging in worked, there is a bad solder point. I have worked on more than few compact Macs and recently worked on five more. Before I even power then up they come apart and every single solder point that involves a connector is reflowed with a bit of new solder. Including at the logic board. The computer can work okay with a cracked solder point, but that point can heat up. I have a couple connectors that are burnt and melted. They only way they got that bad was pro-longed use.

So be careful when checking them. I use a high powered LED and move it around the points and angles to see cracks. Even then they are not always visible which is why I reflow them all then check all the others for caps and such.