Working on electronics that is referenced to the mains voltage is extremely dangerous. Please refer to the usual/local regulations regarding electrical safety. If in any doubt seek out the advise of a qualified person.
I consider this circuit especially dangerous to work on because it has a connection to the metalwork of the whole lamp.
I fixed a TCM 211682 Touch-Lamp. It's a lamp that can be dimmed to three different intensities by touching the metalwork of the lamp. It worked reliably for ages but after the light bulb itself broke and was changed, it just lit continuously and it wasn't even possible to turn it off.
To get to the circuit board the bottom of the foot had to be taken off. There are three screws hidden under a sticky felt material, which I had to partially lift to get to the screws. Once the screws were taken off the circuit board had to be removed from a black case, which said "TOUCH LIGHT CONTROL MODEL: TC-306".
There were no burn marks, so I measured all components in place and quickly found a problem: The Triac BTB04-600SL had gone short circuit. To be sure I had to desolder it and measure it, but it was still shorting out.
I bought a new Triac and replaced it. And it works!
The circuit itself is pretty simple. It uses a capacitive dropper to generate the low voltage for the control chip, which is a COB on a separated board that is soldered-in. It triggers the Triac at different positions in the sine wave to dim the connected light bulb, which is a pretty common way of doing it. The metalwork of the lamp is connected via the brown cable, which is connected to the COB via two Class Y-Capacitors and a 4.7k resistor to generate the touch input.
For the reference: This is what the circuit board looks like from the back (without the Triac):
And a picture of the touch light control module case: