Soldering headers screwed up Trinket?
There are what appear to be burn or melt marks on the 5 pin component labeled QTSO and on the diode near the USB pin. That could be a sign of damage due to soldering, reverse polarity, or excessive current draw through the voltage regulator (a short circuit).

Based on the fact that the light stays on solid when the reset button is pressed,  it sounds like it could also a different issue. First, turn on verbose output in the arduino IDE and post the full output when you try to upload. 

Next, try disconnecting everything except the USB cable while uploading the program. If that does not fix it, it is most likely that the bootloader is corrupted. This has happened to me on multiple occasions for no apparent reason and it is pretty easy to fix. 

If repairing the bootloader does not fix this, it is most likely that one or both of the components mentioned above are damaged.