Not sure I fully follow you but here's what I'm hearing:
You can't get the computer to boot up while connected to your normal computer monitor.
You CAN get it to boot up just fine while connected to your 32" TV. No issues here at all right?
You've got it... no issues booting up to the 32" TCL, which is actually a year younger than the 55" TCL, although it's a 1080p display.
This morning, I simply disconnected the HDMI cable from my PC, powered the PC up and could tell be the busy light that it was booting normally. Three minutes later, I connected the HDMI cable to my 55" display, via my Onkyo AV Receiver, and it works fine.
I've tried booting up with the HDMI cable hooked directly to the HDTV and through one of the HDMI inputs on my AVR... it makes no difference, it won't boot either way from a cold start. I even swapped out HDMI cables and two cables produce the same result.
I was going to try to update my motherboard bios, which will require a flash drive to accomplish from what I'm reading. I have found a case now from someone else who was having this problem, and he was able to resolve it by installing a videoport to HDMI adapter and plugging it into the videoport on his graphics card and the HDMI cable into it.
He says there's something going on with his display device that was putting a constant current drain on one of the cable's lines, even when it was off, as evidenced by a busy LED light on his motherboard that went out when he disconnected the HDMI cable. His theory is the videoport/HDMI adapter is doing something that somehow isolated that signal.
I don't know but I'm thinking this is a BIOS issue either way. Curious to hear what you find out.
I'm going to figure out how to update the BIOS, as I don't think I've ever done it and the computer is four years old now.