I'm not sure why you would assume that the general readership would know what a 42PA30RQ is other than a 42" TV of some kind. And you did not mention how the cable box was connected to the TV (HDMI or whatever).
More than likely, the TV or cable box are set to a resolution not supported by the other device or are set to some specific resolution manually rather than allowing the TV and cable box to communicate with each other and automatically determining what resolution to use.
You could start by unplugging both of them for a few minutes, then start the cable box first and the TV second. Also the cable box may be using a DVI interface even though it has an HDMI connector which means the cable box can't really communicate with the TV so they can't match settings. In that case, the cable box may be outputting RGB and the TV may be set to YCbCr (though that usually produces visible images, they just have extremely BAD color). When there is no image at all, figuring out what is going on can be difficult. You may need to connect your old TV temporarily to see the cable box menu so you can figure out what's going on.