While your OptiPlex 3040 can be upgrade to an i7-6700 processor, the current specifications are already better than Quik software recommendation.

1.  The i5-6500 sixth generation processor is way better performance than a Core Duo or i7 quad core first generation.

2.  The i5-6500 has integrated graphics Intel HD 530, which is capable of 4K playback and is performing well beyond Intel HD 4000 from third generation.  The video RAM is sufficiently allocated from system RAM.

You do not need 3 and 4 or anything else.  Just install Gopro software to your current system and it will be running fine.

@Chino de Oro​ Thank you for taking the time to reply and for telling me my system hardware is sufficient to run gopro quik.

For quite some time now the video playback has frozen.  It must be a software issue then?

Is there anything that I should be looking at?

Thank you so much, 

C

You left out the system storage type information.  Are you using SATA SSD or spinning HDD?

For software, not everyone will feel comfortable to perform a clean install of operating system but that is the best way to get rid of all issues with conflicted drivers, corrupted system files, and incompatible settings.

For hardware, if anything that could improve overall performance in your system would be solid state drive and a discrete graphics card.  Most common choice is AMD RX 6400, for example https://www.amazon.com/PowerColor-Radeon-6400-Profile-Graphics/dp/B09YTB3KH6?th=1

@Chino de Oro​ Thank you so much.  The gopro footage is on an internal SSD (but not the 'C' drive, I store it on a SSD that is the backup, and really only has gopro footage on it otherwise.

I'm very grateful for your knowledge sharing, I'll look at the graphics card.

Thank you so much,

C

Glad to help out.  If you received answer to your question, you can close this thread by marking helpful post as accepted answer.

Remember the upgrade suggestion is for overall system performance improvement.  Not a requirement of GoPro Quik software.  Beside the suggestion of adding a discrete graphics card, I strongly suggest to put your OS (assumed Windows 10) and applications on a 2.5" solid state drive.  You will see the improvement as day and night.

If you have additional questions during the upgrade process, just create new questions and you will receive assistant from community and myself.  You can review this video for the Windows 10 installation process to gain some idea prior to working on your system.  https://www.dell.com/support/contents/en-us/videos/videoplayer/how-to-install-windows-10-using-a-usb-key/6079805044001

There are many different ways to install Windows operating system, review this tutorial blog will also help.