"Rummaging through my old parts box unearthed a power supply that was a bit more powerful than the one that came with the router, and even fit the connector." Is he describing a "wall wart" type power supply? A picture would help. A teardown would help more. There are large numbers of really crappy wall-powered DC supplies available, mostly from China.[1]
Look for a UL approval marking and a UL approval number. That indicates at least some attention to quality. UL is mostly concerned about fire safety, but their basic test for power supplies includes connecting it to a load box at the power supply's maximum rating, then running it for a while to see if it overheats. This catches power supplies with exaggerated ratings.
Avoid no-name power supplies. This is a well-known headache.