If you want to test your theory that it's something wrong with the TV, I'd suggest you try connecting either Blu-ray player up to another TV and see if you can replicate the problem. If you can't, then I'd contact Mitsubishi for your next steps.
My family just received a BD-E5300 to replace an older Sharp Bluray player that stopped working on the TV
After hooking everything up, turning on the bluray player shows the Samsung logo with sound, then goes black. The screen then flickers to blue (which means no input) and then again shows a black screen.
I've tried this with two HDMI cables.
I suspect that this issue is with the tv, a Mitsubishi WD-65738. The symptoms of the last player not working was that it wouldn't play discs due to an issue with HDCP.