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My mother was forced to switch from the traditional Cox main cable box to Contour, and the Contour HDMI connection is apparently not compatible with the HDMI port on her first generation Sharp Aquos HD LCD TV (she just gets a blank screen), forcing her to use the much lower resolution coaxial connection. Other devices, such as a laptop, DVD player, and Blu-Ray player, work fine with that TV HDMI port, and both the picture and sound on the TV are gorgeous, and worked perfectly with the old cable box, so she's not about to replace the TV. According to the tech who came out to troubleshoot, the issue is apparently with the overly sensitive HDMI port on the Contour boxes. Is there another type of box with alternate connections (i.e. DVI, composite, etc.) that Cox can provide at no additional charge? She's already paying around $200 per month for TV, internet, and phone, and that's without having any movie channels or a DVR; and since it was Cox's choice to force the box change, the problem is on their end.
An "overly sensitive" port doesn't sound very technical. Cox has issued me receivers and equipment with faulty ports, so that'd be my first suspicion. If the replacement box is still "sensitive," there are Contour receivers with outputs for component cables.
I can only suspect "sensitive" to mean an issue with piracy or encryption: High-bandwidth Digital Content Protection (HDCP). Perhaps the Aquos doesn't support the HDCP version Cox uses to protect content. I haven't tested but I've read an HDMI splitter would bypass HDCP.
The TV only has one HDMI port, so there aren't any others to test. I did try testing multiple cables, from the original generic HDMI cable that came with the TV all the way up to a high end braided high speed HDMI 2 cord, with the same results. The tech swapped out the Contour box with another box of the same model and it had the identical issue. He said he couldn't use a different Contour box with additional connections because the only one he had was the DVR box, and Cox would charge extra for it. The only thing I haven't tried yet is an HDMI splitter as suggested by Bruce, that may be my next step.
I would suggest looking to see if there a firmware update for your TV. Do you have the exact model number? Something like LC40D78UN.
If there are no updates or your first-generation Aquos doesn't have an Internet connection, I'd reset the TV to its factory-default settings.
The TV may be still retaining...or failing to release...the authentication key for HDCP encryption from your previous cable box. A reset may clear the old key.