The fact that your previous TV had no problems like this could easily indicate a problem with the TV, but before I exchanged it, I think I'd borrow another BluRay player from a friend and see if you get a similar result. You might also try different HDMI cables.
With these technologies, odd incompatibilities can easily crop up.
You didn't mention the model of your Bluray player or its age.
Anyway - before sending the TV back for an exchange, I'd say you're on the right track with your troubleshooting, but you haven't quite carried it far enough to conclusively convict your TV.
It would be a real drag to replace the TV only to discover that an HDMI cable was the culprit.
So, think like Sherlock Holmes, test carefully and write down what you tested and the results so you don't get confused.
One last note: A friend's Philips LCD started having a problem with the TV recognizing the BluRay player on occasion. It became more frequent until one day, the TV no longer recognized the BluRay player on any HDMI input and then a few weeks later the TV died. The point is that something is going on and you need to get to the bottom of it before the exchange period on your TV has passed.