CPU Temperature Overheat

Thanks okay I get it now
Have you reinstalled the old cpu cooler yet ?
And which one was the old ?

Now the CPU is sitting squarely on the heatsink?? just make sure it is and is not caught on anything that stops it fitting flush down.

Now I personally like to use Arctic Silver products to a) clean and prepare both surfaces (this makes them exquisitely clean) then b) apply the thermal compound thinly and evenly over each surface using the index (or whatever) finger in a vinyl glove then c) place a rice grain sized spot of thermal in the centre of the CPU.
Spreading the thermal first makes absolutely sure that every part of each surface is covered but it only has to be very thin the spot of thermal will "bleed" out towards the edges after a few minutes running.
This Arctic Silver Incorporated - ArctiClean then this Arctic Silver Incorporated - Arctic Silver 5

Otherwise lie the others I would be suspecting something in the BIOS - just as a by the by how old is the CPU?? it looks to be new but just curious.

It is seated fine. I'm unable to move the pump block. The CPU is about 4-5 years old now and still works fine. Like I said, it's just saying its overheating when in reality it's not.

The jumper is on the right pins. (The first 2 pins, not the 2nd and 3rd.)

I tried to manually but I wasn't sure what the vcore voltage should be. I know the CPU Voltage should be 1.34v. I'm very uncomfortable with keeping the system on with it beeping away at me telling me it's overheating. Like I said, if it truly was at 127C it would shut down instantly as it used to upon hitting 90C.

I just don't feel comfortable keeping my system on whilst it thinks it's overheating. It takes a couple of minutes to find all of the appropriate values (voltages) and in that time it could actually damage the CPU, y'know? I'm just being careful as this system is the first gaming system I've ever built (for myself). I cherish it very much.

it's just saying its overheating when in reality it's not.

Well that smacks of a malfunction of either the thermal sensors within the device or receptors on the board.

Another thought is have you checked outthe PSU see my ditty on checking the rails it could be out of whack though if it were out of whack that much it should shut down.
Using HW Info
PART A:
You can test the volts on the PSU with HW Info HWiNFO, HWiNFO32/64 - Download < download the right bit version and close the right hand window select Sensors and scroll down to the power section where you will see what the volts are doing see my pic. In my pic the section (Nuvoton) with VBATT is a dead give away you are in the section for the rail voltages. There are other section titles and one that pops up often is ITE
Now the voltage on the different rails have to be within 5% =+/- of what is required or the machine will not work properly if at all.
Limits +/-
12v = 11.4 – 12.6v
5v = 4.74 – 5.25v
3.3v = 3.135 – 3.465v
The Power good signal voltage at pin 8 on the 24 pin plug (grey cable) should be the same as the 5v rail reading/s
See this for the rail voltage info
Power Supply 101: A Reference Of Specifications - Power Supplies (Section 2.)
The original right hand window shows the machine running and is handy for that but for looking at the components in some detail close it and use the main left hand side panel
FOR OTHER COMPONENTS
PART B:
Open each small square with + in it on the section the components are in and then click on the individual component/s (it will highlight in blue) - in the right hand side will appear all sorts of details including brands speeds and other essential info that particular device. See pic for example.

I cannot boot into Windows because of the "overheat". I simply cannot boot into Windows. I've had a new cooler (Corsair H90) purchased and will try that as I've read countless issues with this cooler from people. If it continues after installing this new Corsair cooler then I may have to RMA my motherboard. I may have "scratched" something on the back of the board when I was trying to remove the sticky adhesive/sticky tabs from the old back socket bracket. I'm not sure if that may be the problem.

Depending on what you used to get the original back plate off with could very well of damaged the mobo
Plastic and alcohol is what I used with an Acer back place that I swear was super glued on