I got my broken laptop back today.  It took 12 days round-trip to have the repair do nothing.  While I was waiting, I ordered an off-brand power adapter from eBay for $13, shipping included.  I plugged it in and it works.  The power jack is very use, but for now it is working with the new adapter.  By the way, a replacement adapter from Toshiba is $99.

When the jack eventually completely fails on my Satellite L305, I will replace it with one from Radio Shack.  I made the same fix to my wife’s Satellite A135 last weekend and it is working just fine now.