Did it work OK before installing the new power supply
OR was the new PSU installed in the belief that the existing fault was the PSU

 

Recheck your connections. make sure you used the correct connector for PCI-E to your Video card not just any 6 or 8 pin cord. Also make sure your main power to the board is fully seated and your using the CPU power connection on the board as well (usually 4 or 8 pin). As mentioned above I hope you didn't just jump to the conclusion of a bad supply even though having a spare supply is a nice thing. Proprietary Power connections are not a big deal any more but not mentioning how old your PC is doesn't help there.

 

I noticed the power supply is fully modular
I suggest you recheck your connections as listed in the manual
http://www.corsair.com/en-gb/rmx-se.../en-gb/rmx-series-rm1000x-1000-watt-80-plus-gold-certified-fully-modular-psu-eu

Installing your NEW RMx Series

Step A: Removing your existing power supply

If you are building a new system, skip to Step B.

1. Disconnect the AC power cord from your wall outlet

or UPS and from the existing power supply.

2. Disconnect all the power cables from your video card,

motherboard and all other peripherals.

3. Follow the directions in your chassis manual and

uninstall your existing power supply.

4. Proceed to Step B.

Step B: Installing the Corsair RMx Series power supply

1. Make sure the power supply's AC power cable is not connected.

2. Follow the directions in your chassis manual and install the power

supply with the screws provided.

3. The main 24-pin power cable has a detachable 4-pin

mechanism in order to support either a 24-pin or a 20-pin socket

on the motherboard.

A. If your motherboard has a 24-pin socket, you may connect

the 24-pin main power cable from the power supply

directly to your motherboard.

B. If your motherboard has a 20-pin socket, you must detach the

four-pin cable from the 24-pin connector, and then plug the

20-pin cable onto your motherboard without connecting the

four-pin connector.

4. Connect the eight-pin +12V (EPS12V) cable to the motherboard.

A. If your motherboard has an eight-pin +12V socket,

connect the eight-pin cable directly to your motherboard.

B. If your motherboard has a four-pin socket, detach the

four-pin from the eight-pin cable, and then plug this

four-pin cable directly to your motherboard.

5. Connect the peripheral cables, PCI-Express cables, and SATA cables.

A. Connect the peripherals cables to your hard drive

and CD-ROM/DVD-ROM power sockets.

B. Connect the SATA cables to your SATA SSD or

hard drive's power sockets.

C. Connect the PCI-Express cables to the power sockets

of your PCI-Express video cards if required.

D. Connect the peripheral cables to any peripherals

requiring a small 4-pin connector.

E. Make sure all the cables are tightly connected. Be sure to save

any unused modular cables for future component additions.

6. Connect the AC power cord to the power supply and turn it on by

pushing the switch to the ON position (marked with "I").

WARNING: The detachable four-pin from the 24-pin main connector is not a "P4"

or "+12V" connector. Serious damage can be caused if you use it in place of a "P4"

or "+12V" connector.

It is possible to have the wrong cable connected

 

Do you still require help please
If not mark the topic solved by clicking the mark solved button on your post

 

Did it work OK before installing the new power supply
OR was the new PSU installed in the belief that the existing fault was the PSU

The new power supply was installed on the assumption that the existing fault was the PSU. Before the install, the computer would run for roughly 5 minutes before the screen would go black with no video exput, but all internal lights and fans remained on.

 

Recheck your connections. make sure you used the correct connector for PCI-E to your Video card not just any 6 or 8 pin cord. Also make sure your main power to the board is fully seated and your using the CPU power connection on the board as well (usually 4 or 8 pin). As mentioned above I hope you didn't just jump to the conclusion of a bad supply even though having a spare supply is a nice thing. Proprietary Power connections are not a big deal any more but not mentioning how old your PC is doesn't help there.

The PC was built roughly 3 years ago, and I've tried using different cords in different places to no avail.

 

I noticed the power supply is fully modular
I suggest you recheck your connections as listed in the manual
http://www.corsair.com/en-gb/rmx-se.../en-gb/rmx-series-rm1000x-1000-watt-80-plus-gold-certified-fully-modular-psu-eu

It is possible to have the wrong cable connected

I will try this again in the morning, thank you.
I'll post again if it doesn't work, or mark as solved if it does.

 

You might consider putting the old supply back in and running Memtest86 as a boot flash drive or CD (if you have the ability to do that). memtest86 is a very small application and seems a waste to go the CD route. If you can stay up for 10 min. at a time you should be able to download the tester and get it onto a flash drive or CD before the PC fails. Then boot up to the CD or Flash drive and run the tester to see if it detects any memory errors. Something more simple you can try if you have more than one stick of memory is to remove them one at a time leaving just one in the first slot and test to see if the machine runs or fails with each stick. That's a manual way to find a bad memory stick. You might also want to check your system temps to see if it's shutting down because the CPU is overheating. An App like CPUZ or Speccy might help. You can also look in the event viewer to see if there are any faults occurring in the System.