No, that's very unlikely to work, even if you do manage to find another one with the same connector.
The box you're looking at is not just a junction box, it's also the power supply for the LEDs - and it's specific to the type and number of LEDs in the fixture.
TL;DR Your Dimmers are Not Compatible with the Bulbs
Older dimmers don't work with most LED lights. Period. Many newer dimmers work together with newer "Dimmer Compatible" bulbs (as yours are listed). There are even some dimmers available today that are not LED-compatible, and 2013 or older dimmers are very likely to be not LED-compatible.
PCs, especially cheap PCs, have pretty big power supplies. The "850
watt" power supply actually draws over 1200 watts. It sounds like your
PC is simply too much for the system. It may be necessary to downsize
the PC, maybe get rid of performance video cards, get a smaller power
supply, etc. One of the "micro-PCs or a Mac Mini would be a great
An LED bulb with appropriate base should be perfect. Some LED bulbs have oversized plastic bodies that might not fit well in a fridge's compact light fixture so pay attention to the exact size and shape when buying.
Chances are that the the USB power and the AUX output of your TV share the same 5V power rail. When you connect the LEDs, you either overwork the power supply or some power modulation from the LEDs makes it's way through the power rails into your audio output.
One thing you could try to decouple the audio output by using a isolation transformer. Something ...