Why are files damaged (become broken) when copying?

Question

Windows

About six months ago, I began to notice that some games (repacks) during installation give an unpacking error due to a damaged archive. At first I sinned on the torrent, I thought it was downloading incorrectly with hash errors. Partly I was right. Yesterday, for a test, I downloaded the Windows 10 Technical Preview image from the official site (by default, chrome loads in C, I copied it to D). Then I decided to check the hash sum, just in case. Checked with the HashTab 5.1.0 utility. It turned out that SHA does not match. I thought it was better to download a torrent. But then for some reason I wanted to check the hash of the source file that was downloaded to drive C. And its amount coincided with what is indicated on the Microsoft website. I deleted the copied file from drive D and copied from drive C again. The amounts didn't match. Then again, to another physical hard drive. The same. Furthermore, often even the hash sums of the copied files did not match. Those. the file was copied a little differently almost every time. The file sizes match byte for byte. The image after copying opened normally, the files are visible in it, but they cannot be unpacked, an error appears. About 10 times I managed to copy it with the original hash sum. I tried to copy Total Commander - the result is the same. Continuing testing with horror, I discovered that all files are damaged in this way when copying: games, movies, music! The smaller the size, the less likely it is to be damaged. I don't see this problem on another Windows 7 PC. but it is not possible to unpack them, an error appears. About 10 times I managed to copy it with the original hash sum. I tried to copy Total Commander - the result is the same. Continuing testing with horror, I discovered that all files are damaged in this way when copying: games, movies, music! The smaller the size, the less likely it is to be damaged. I don't see this problem on another Windows 7 PC. but it is not possible to unpack them, an error appears. About 10 times I managed to copy it with the original hash sum. I tried to copy Total Commander - the result is the same. Continuing testing with horror, I discovered that all files are damaged in this way when copying: games, movies, music! The smaller the size, the less likely it is to be damaged. I don't see this problem on another Windows 7 PC.
If who faced, prompt, with what the similar problem can be connected. I myself sin on iron: the motherboard or memory.
PC configuration:
OS: Windows 8.1 x64
MP: ASUS P8P67 LE
CPU: Intel Core i5 2500
RAM: 16GB DDR 1600Mgz
HDD: 2x Western Digital WD10EZRX
Anti-Virus 2015, before that was 2014. No viruses.

Answer 1

I would not trust one antivirus, I would check with livecd and liveusb, I would run memtest RAM, I would check the quality of the Internet for failures

Answer 2

The problem was in memory. One of the four bars is broken. It is strange that the OS worked fine and did not issue a BSOD. Built-in ASUS MemOK! I also thought everything was fine.
PS Memory 3 months, CMX4GX3M1A1600C9 ver.8.16