I'd start by looking for the most likely causes, so a process of elimination. This doesn't completely rule out faults or issues elsewhere, but it's an approach that saves us taking the car engine to bits when the the fuel needle is on E.
You didn't have the issue with the Denon when it was new, so it's unlikely to be that.
Aside from changing out the amp a year ago, has anything else changed in the room in the last two weeks?
The sub is 14 years old.
The cable is under the floor - does that mean it's sandwiched between the floor proper and a solid floor on top, or is it dangling in the crawl space and possibly sitting in ground water? Has that been this way for 14 years too?
My first instinct would be that its capacitor-related in the subwoofer. We know caps don't live forever, and also that they don't like heat. Depending on the circuit design one or more caps could be near the heat sink for the output transistors and been gently cooked over the last 14 years. Before you start diving inside the sub though we should rule out earthing and connection cable issues.
As a temporary test, try moving the sub next/near to the amp and connect with a shortish phono cable. Also, plug the sub in to the same power sockets as the amp is getting its juice from. Your problem isn't low level hum, so this isn't a ground loop issue. Plus, your AV receiver might not be earthed through the mains cable anyway. It's likely to be Double Insulated and have a Floating Ground which basically means there's no earth connection through the mains plug because everything hazardous has two lots of insulation inside. If you're still experiencing these rising tone issues then it's a safe bet that it's a dying capacitor.
Your sub's power supply converts AC mains to lower voltage DC for the amp circuit. Capacitors are used in a few different places. There'll be some big-ish ones in the amp stage to act as power reservoirs. There'll also be a few smaller ones in the power supply to stabilize the voltage rails and decouple power rails from ground. If those ones are starting to die then the effect will be the same as putting your thumb across the pin and ring of the phono lead before connecting to the receiver. If the sub is on there'll be an almighty hum. Sound familiar?
You can check for dying caps visually. A good clue is that the tops go domed. That's because the insulation material inside has expanded. Sometimes you'll see it burst out from the bottom of the cap where it connects to the circuit board. Occasionally you get caps that have dried out. That's harder to spot since the effect is for the internals to shrink.
Luckily for you the caps are going intermittent rather than have died completely, so you can use a couple of diagnostic tricks to help pinpoint the issue.
Intermittent caps hate the cold and they love heat. If there's an intermittent fault then using a can of freeze spray to chill a capacitor will make it fall over. Gentlt warming will revive it. A hair drier or paint stripping hot air gun will do. Be careful with either. You don't want to cook anything. Freeze spray does cause condensation, so don't go mad with that either as you could short out the board if you turn it in to a frosted winter wonderland
It almost goes without saying too that if you've got the sub open and are messing about like this then inevitably you're exposing yourself to 240V mains. Be bloody careful.
Replacing caps requires soldering skills and the tools for the job. If that doesn't sound like you then it's either time to put the sub in the hands of a repairer or look for new.
Spec'ing replacement parts: With caps, you need to stick to the same voltage and go for the same capacity or higher. The ratings are written on the caps. They also have a temperature rating; either 85 deg C or 105 deg C. The lower temp ones are cheaper. If your sub has lasted 14 years with 85 deg C caps then don't bother upgrading to 105's unless the cap is right next to a heat sink. If the orignal part is a 105 though then replace wth the same heat rating.
