Since the hum level doesn't change with the gain or tone controls, the culprit is in the amp's internal sound path. This probably won't be trivial to debug.
The problem might be a bad ground connection or failed component in the amp. Since the amp seems to work OK other than the hum, it's possible that the main path through the amp is OK and a side path has a problem. If you have the current TNT 115 it looks like there are a number of things to check out - it has a built-in chorus and an electronic crossover - so see if the hum level follows the gain controls on those functions if you can.
Also, there are a lot of patch jacks on this amp - the electronic crossover outs as well as a preamp out and power amp in. I'd be really suspicious of the preamp out and power amp in. Those jacks are set up with a switch which is thrown when you insert a plug (e.g., when you use the preamp out jack, it not only feeds the output, but disconnects the preamp from the power amp internally). If those rarely used jacks have corrosion, the switching function often introduces some noise. So, I'd try inserting and removing a plug in these jacks (power off, please!) to see if you can make sure they are clean.
In most newer amps the preamp components are ICs (sometimes even in the power amp) and the wiring is all in a PC board, so a failure in a chip or the board will be hard to correct.
Write back if that doesn't work,
David Fung