Apparently Netgear had under estimated the voltage these should handle so a 6.3V 1000µF piece wasn't enough. Down to Halted I went and grabbed some 10V 1000µF capacitors. I grabbed my trusty desoldering wick, soldering iron, and solder and replaced the busted caps with the new ones I had purchased.
With that all together I plugged everything back in and to my delight it started working again! Now hours later (I wish Halted were closer) I can start my day.
Technologies: Basic Electronics, a soldering iron