4K videos and their 'rips' are typically using the h265/HEVC video format. That format is not supported by video acceleration on your GTX660, so the i7 2600 has to step in. Unfortunately, CPUs are not nearly as efficient to handle today's video formats. So hiccups will appear as also audio streams need to be handled as sometimes converted. Proper hardware acceleration for h265/HEVC started with the GTX950+ series for Nvidia.
Nowadays, just about every new CPU can handle that format. The next-gen format AV1 is now the new challenger. Furthermore, it's not just the resolution of 4K. There is also the bit format (10bit, 12bits) as well as the latest craze, HDR, which comes is a variety of versions.
Some cheap Android boxes are set up to handle most/all of that video stuff, but if you are fixed on PC hardware, getting a new Intel CPU with internal graphics will get you a long way. AMD apu's can also do the job, but I have no firsthand experience with those (yet).
Which OS are you planning to use on the new hardware?
Specific lockups can only be investigated with a provided
debug log (wiki). Hearsay doesn't help us.