One common reason for hash failures with BitTorrent transfers is that something is corrupting the data, which could be either a rogue BitTorrent source (e.g. someone with a rogue BitTorrent client deliberately sending corrupt data to interfere with transfers), faulty RAM or a problem with the hard disk or motherboard. Most direct downloads do not carry out hash checks, so this may explain why normal downloads go fine.
Try running memtest (link). Alternatively, try running BitTorrent on another PC (e.g. borrow a laptop) to rule out your PC's hardware.
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