No, you don't need to copy the files to the C: drive. Several problems appear, if the files come from external drives, especially storage cards, so it is important to work from an internal HDD. You said, F: is internal, so its very good and not part of the problem.
The codec pack is good, but maybe not good enough. MOV is a video container format, that was used by quicktime, which comes from Apple. So it is the best to install quicktime itself, or quicktime light. MOV is a container format, that means the video part is coded in differnet codec formats. The most popular in consumer context is H.264, which is also used in the MP4 format. Professional cameras shoot in RAW format, e.g. ProRes RAW, which is, as far as I know,also containered as MOV. There are more formats on the market. MediaInfo (free) gives you information about the codecs of the media file.
Consider to convert your files to a more supported format. There are many good converters available. They should be free, don't pay for it, except you get more value. You can find many converters for dollars, that bring exactly no more value. Proposed in this forum is "Handbrake" (free).
Have a look at magicYUV, a codec, that converts your video lossless. In PD16, it is incredibly fast. Disadvantage: as it stores every frame as full picture, the rsulting file is incredibly big. No problem to get a 100GB file after converting.
Hatti
Win 10 64, i7-4790k, 32GB Ram, 256 GB SSD, SATA 2TB, SATA 4TB, NVidia GTX1080 8GB, LG 34" 4K Wide, AOC 24" 1080