I had this problem too. I've just fixed it today.
The problem seems to be the power adaptor. The Slingbox itself is fine. If you try replacing the power supply, you should find all the lights come back on OK.
I used a special power adaptor that allows you to change the voltage to the same as the adaptor that's broken, but I presume it won't be too hard to find
You can try to use a new power adapter for your Slingbox SOLO in order to determine if this is the root cause.
If it does not work, you can check this link and follow the recommendations.