The logs with dates shown as 2013 (#47-51) were created after the battery had been removed from the ST16 or it simply ran out of power. If power is lost on the ST16, the dates reverts to the default of 12/31/2013. After the date was reset, the ST16 was connected twice (#51-52) but only for about 20 sec.
The last time the ST16 was connected to the H, it did acquire a good GPS lock. I suggest giving it another test outside in a grassy area with a clear view of the sky. Remove the camera. If it transitions from Acquiring to Ready, watch it and see if it stays locked. If so, go to a hover a few feet above the ground and continue to watch it. If the GPS stays locked then it may be good. I suggest a couple of flights w/o the camera mounted to make certain it is airworthy.
The Flight Controllers on the H are very sensitive to overheating. So avoid turning it on when the temp is higher than 85 if the sun is out. Also be careful not to store the H in a hot place such as the trunk of the car. The FC can be permanently damaged if it gets too hot.