in the automotive world, larger electronic components are either glued in place or potted in encapsulating compound to eliminate vehicle vibrations from working them loose from the circuit board. That small yellow square left of the capacitor is a transformer and provides a good anchor to glue the cap to it. In electronics and especially in portable or mobile devices, all electronic components MUST be physically or mechanically welll attached to the circuit board or to a strip, etc. before it is soldered. Soldering provide nothing but the electrical path for connectivity. Solder is too soft to support heavier components and when poor mechanical anchoring is used, often the components will break loose from the solder pads. The replacement capacitor can be glued in place using a hot glue gun and the matching glue sticks. As for the transistors, the newer replacements look to be substantially larger w/ built-in heat sink on their backside to handle the current that apparently GM under estimated. The small circuit board you have pictured is a power inverter board which mounts to the main instrument cluster board, not the standard power supply type as often thought of.
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