No power to one spark coil

If I understand it, you had a misfire already and while trying to find it you swapped the coils around? Now are you saying that you put the coil on number one and the coil didn't work or that the connector at cylinder three was broken?
If unplugging, it from three made no change then check the wiring to the coil first. With a cheap common test light connected to battery positive you should be able to test a few things. First touching the black wire in the connector should light up, that is the coil ground, next the brown wire should cause it to light up as that is the ground in the ECM, and if you start the engine and touch the dark green with white wire the light should flash as the control wire grounds out through the ECM. Now connect the test light to ground and touch the pink wire with the black stripe, which is battery power with the key on the light should light. If these all work the coil itself is likely bad. These coils share the power, ground and ECM low feeds so if one of those doesn't work at the connector the wire crimp or the short lead from that connector to the next is likely bad or broken. The other issue with this system is the coils can short out internally and then damage the control transistor in the ECM. If the light doesn't seem to flash when you touch the green with white wire, it's possible the ECM is faulty.

Let us know what you find. The HHR is a unique vehicle and GM sort of abandoned them parts wise. I like to keep them alive if possible.