well, before we assume a connectivity issue are you sure that the pc itself is starting up correctly? a checklist of various things to check below followed by a list of things commonly wrong for connectivity.
-please note if this was a prebuilt or homebuilt and list your specs or model for reference here. also list if you have a warranty in case we determine its a hardware problem. (you can double check all of this once your monitor arrives.. if it still doesnt work its not the tv's fault).
-does your pc appear to boot correctly and stay running (do lights and fans all come on, etc)?
-if not, check that you have installed all power connectors.
-are there any red or other ominous looking (check manual for error leds) or an error code (on models with lcd panel on them) that indicate error?
-if you have a motherboard speaker hooked up does it beep?
-have you tried removing the video card (while off) and plugging the hdmi into the motherboard instead (testing for dead gpu)
-if the above worked try reinstalling the video card making sure that it is seated correctly in the slot. make sure the power connectors are all connected.
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-make sure you are using the correct input - that the input selected is the same port you are connected to in the rear. note: you may need to restart the pc if you swap inputs while it is booting as it may have a hdmi handshake issue.
-if your tv has a special PC connection use that.
-try running with 120/240hz modes turned off (use 60hz mode).
-try running with a hdmi cable you know works on other devices.
-make sure the tv is on FIRST then turn the pc on afterwards (hdmi handshake issues).
-like the above, if that doesnt work turn off the tv then turn it on again while the pc is still on.
-try all gpu ports.
-as in the first list, try just the motherboard with gpu removed.
i think you need to try the above and give us a response to each of the punchlist items so we can try and narrow down why its not working.
for reference, i personally use a tv as my main monitor on my desktop, and maintain both a desktop and two laptops which connect to two other tvs. generally other than some simple problems like hdmi handshake and faulty cables connectivity is very easy and works every time.