My daughter wanted a guitar last year. I scanned Craigslist and found a nice lefty MIM Strat. I also spotted a used Peavey Rage selling for a reasonable price that looked perfect for a beginner. When I got to the seller house and tried the amp there was a terrible noise. I wiggled the jack and it started making even more noise. I assumed it had a loose solder joint on the PCB. A lot of modern amps have the input jacks mounted directly to the board. Flying leads (when the jack is mounted to the chassis and wires are run from it to the board) are more common in older amps. Not wanting to have to make a repair on maybe have more to deal with I said I would pass on the amp. The seller kept dropping the price as I walked away. I told her the repair is pretty simple and she will probably be able to sell it but she should add that it has a shorted jack to her listing. In a last ditch effort to move the amp she asked "will you take it for $15. I just want it gone." At that price I figued it was worth a gamble. When I got it home I pulled it from the cab and reflowed the solder joints for the jack. It took maybe 5 minutes and most of that was just waiting for the iron to heat up. I fired it up and it was as good as new. It's pretty much that simple.
Regarding the filter caps in tube amps, you are correct. They store a high voltage charge like a battery even after the amp is unplugged. I find the easiest way to discharge them is to play my guitar through the amp and pull the plug from the wall while still strumming the guitar (with the amp on) until the sound fades completely. Then I unplug the amp and pull the chassis and connect a wire with an alligator clip on one end to the chassis and VERY CAREFULLY touch the other end of the wire to each terminal of the big electrolytic caps in the amp (the one's that look like big metal cans). I do this with one hand at my side. Putting one hand on the chassis and touching something with a charge would cause the voltage to discharge across your heart. Talk about riding the lightning. Instant defibulator.....not good at all and something to avoid at all costs. That discharges any remaining voltage. I even made a tool for doing this by mounting a 10W wire wound resistor inline in my discharge wire and covered the whole shebang with shrink tubing. I put alligator clips on both ends. The resistor helps knock down the spark if there is a little more than normal voltage in the cap I'm discharging. Typically the caps only have a few volts after using the pull the plug method so I've never really encountered sparks. Some dudes just do it with a long screw driver and let the sparks fly.

I wouldn't dream of doing that. Then check the caps for voltage with a DMM before touching anything. If you are unsure of your ability to do this take it to a pro. Fear is good...it keeps you on this side of the grass. The problem you are describing is a minor, inexpensive repair and is a pretty common issue with board mounted input jacks.