That's a bit weird. If it's giving you "No Signal" messages across multiple TVs then either your cable is broken, or the console is. It sounds like it's either the HDMI port itself, or an internal fault that's knocked out your console's video output.
If you have any kind of warranty with the store you bought it from, you could take it back to them for a replacement. Or you could try contacting customer support, though they will probably charge for an out of warranty repair if it's over a year old.