If all of the lights are out, this makes me think this is an issue with your Power Supply Unit for your Slingbox. There should be no reason that the Power Light should be off, unless this has either gone bad or is in a non-working outlet. I would recommend unplugging this fully from the back of the Slingbox and plugging this back in, making sure this is sitting nice and snug in its port.
If at this point, the power light still isn't on, it would more than likely be an issue with the Power Supply itself, like I mentioned before. You can purchase a new one at the link below:
Since you've only had this a few weeks though, you may be able to have this replaced for you if the unit is new or still in warranty. You can reach out to support by visiting the link below while logged into your account:
I hope this helps!!