Hummm, hard to open a 6646, normally they don´t present any troubles, but there are things that can be broke or lose by a hit. To open it check the sides of the transformer, just above the line that seems to divide the case into to halfs there are 4 round "shadows" on the sides(two each), i think that with the right, marklin hidden tool, they can be pushed to release the inside clips that holds the two halfs together, in my case i just drilled of, and later replace by ohers plastics cylinders to close the transformer again .
Once opened check for the inside of the rear connections, because they can be lose, also check a proper contact between the inside part of the knob control and the bobine.
Of course you can always go the Marklin dealer if you don't want to void warranty or you're not sure of what you gonna do.
Mine, a 6647 actually (230V) had the L rear plug lose and i had to open the whole thing to fix it and get a proper connection
Bye
Francisco

it seems i forgot the step one of any troubleshooting guide:

"is your device properly connected to the electric supply?"[:p]

Sounds like it, yes... I have never seen this before, but it is of course possible... One of my old 60:s transformers had some fault in the variable resistor after a while, but that "while" was 8 years or so and it was only within a very limited area of the whole span...

Hi Varun, the "rivets" are some kind of plastic lock. You can drill a 1.0-1.5mm hole, then insert a small screw and pull firmly from it.
If you're lucky, the rivets will be reusable.
Once open, check for a good contact of the cursor against the coil, it could be loose. This failure is common. Also check the wire from cursor to the red output connector, sometimes y brakes.
Regards,

Hi Varun, glad you could repair your transformer, as for the rivets, they can be easily replaced by anything with the same diameter, in my case some wooden sticks for cocktail purposes...
Bye