This doesn't 'scream' like a PSU problem to me, going to be honest...Let me break down why i feel that way...
The PSU supplies 'clean' electricity for your rig... typically when a PSU is going bad, its a pain in the ass to diagnose... the reason why is the symptoms are that of 100 different things... usually what happens if when your computer is under load with a bad PSU, the power level will dip and spike causing a BSoD, application hangs/crashes, or even cause the computer to just shut off...
Graphics cards are usually the most PSU intensive component, which is why i can see everyone pointing to the PSU, BUT:
1. max wattage for a PCIe x16 slot is 75W (which isn't much) and thats if nothing is in any other PCIe x4 or x16 slots (if so, that drops to ~35 watts)
2. Per Tom's Hardware, the idle wattage consumed by the AMD RX 460 is 13.2 watts, which is virtually nothing and shouldn't be enough to crash computer on a bad PSU. (source: https://www.tomshardware.com/reviews/amd-radeon-rx-460,4707-5.html_)
What I think likely happened is there was an electromagnetic discharge either during cleaning or while pulling out the card that fried the card or the port... You can have you're PSU tested, but keep in mind, Best Buy wants to sell you a PSU, if there is even the slightest variation in wattage or efficiency, i wouldn't doubt they would fail it (even if its within the PSU acceptable parameters)
I hope this helps, but you're due for a GPU upgrade anyway...you can get a nice 1060 for a little over 200 bucks right now and the prices are dropping...