The cradle is actually an overly simple, even stupid, design, and is prone to failure. You may be able to fix it on your own. If not, any moderately competent electrician can fix it, and even improve it.
The way the cradle is supposed to turn on is that when you insert the cartridge into it, it pushes down a flimsy bent metal strip to make contact with the circuit board. This is the switch judb means. It is the most primitive of switches. Because the strip is so flimsy, it can easily get bent out of the angled shape it is supposed to be in. When this happens, the result is no power.
If you look into your cradle where you insert the cartridge, you should be able to see the metal strip. If you push down on the strip with your finger, the green power light should come on. You need to put it back in the right shape so the DMS makes proper contact with it. It's easier if you take the cradle apart. I can't explain it any better, but once you see the strip you'll be able to figure it out for yourself.
What I ended up doing with my cradle is giving it to the handyman in my office. I explained to him how it's supposed to work and asked if he could come up with anything better. He ended up installing a proper power switch on the base of my cradle, so I don't ever have to worry about the internal switch breaking again. Works like a charm.