This thread is started to provide others with a solution that I found after troubleshooting problems with my Panasonic TC-P50ST60. The solution should work for other plasmas and TVs as well, since this solution addresses a unique problem that does not originate with the TV itself or the external device, but rather the HDMI cord itself. When buying a brand new HDMI cord, it is unlikely that you would think to troubleshoot the cord. Consequently, I hope this helps anyone who was in the same situation as me.
After purchasing my Panasonic plasma, I purchased super thin HDMI Cords. However, every time I tried to connect the HDMI cord from the TV to my Apple TV or Mac Mini, the TV continuously reported that there was No Signal and I should check the connections. After going crazy, I finally discovered that there are some manufacturers of HDMI cords that produce HDMI cords that are "directional". What does that mean? Well, it means that one end of the HDMI cord is the "Source" end and the other end of the HDMI cord is the "TV" end. If you accidentally ignore which one is the "Source" end and you plug the "Source" end into the TV's HDMI port, then you will never get a signal on the television. Since the Source end is supposed to be connected to the external device (Mac Mini, Apple TV, blu-ray player, etc.).
I discovered this problem after I ordered MonoPrice's Ultra Slim Series High Performance HDMI® Cable w/ RedMere® Technology. I simply presumed that you could connect either end of the HDMI cable to the TV. However, this was not correct. So if you ever rack your brains over this type of issue and can't figure out why the TV or the external device is not giving or receiving a signal, do not rule out the HDMI cable. It can actually be the source of the problem.