The simplest, and most common reason for HDMI® problems is that either the source, such as a DVD player, or the display, such as a TV screen, is not set to use HDMI® signals. A particular source of this problem is cable boxes that are set to use an analog connection by default. The solution is simply to access each device's menu settings and choose the correct option, which may be listed as HD or HDMI®.
One of the most annoying HDMI® problems is white dots appearing on the television. This resembles the type of interference that appears on over-the-air TV broadcasts during bad weather. In fact the most common cause of this with HDMI® is an older cable not being capable of carrying all the data in the signal. The white dots are where the relevant picture information has not been carried. The solution is to make sure to use modern cables, which will be listed as compatible with at least the HDMI® 1.3 standards.
Another common source of HDMI® problems is with HDMI® switchers, which allow multiple cables to use a single socket, usually on a television. These work by devices sending power signals to tell the switcher when their input should be passed through. This can lead to problems with HDCP, the digital copy protection used on HD sources.
Each device must complete a "handshake" to confirm that it is HDCP compliant. If one device is not compliant, the other will shut down the connection. With a switcher, all the devices must be compliant and a single failed "handshake" shuts down all connections. Sometimes legitimate HDCP devices fail to complete the handshake. If this happens, it can sometimes be cleared by rebooting devices, or disconnecting all the devices and trying them one by one in order to isolate the problem.
One supposed solution to HDMI® problems that rarely works is to buy a more expensive cable. With analog systems, this is a valid solution as a better quality cable will usually mean a stronger signal gets through, lessening the likelihood of poor quality picture or sound. As HDMI is a purely digital format, there are no degrees of quality or strength in the signal. Either it gets the information through or it doesn't. While extremely cheap cables may be poor quality, a well-made cable will work exactly the same regardless of its price.
It is possible for a damaged cable to mean no signal gets through at all. Damage is more likely in a cheap, poor-quality cable. If there is no picture and all other possibilities have been eliminated, it is well worth trying a different cable to see if that was the problem.