Windows 8.1 installation on non-UEFI machine fails with error 0x80070570

I am trying to install Windows 8.1 on a clean (formatted) partition on an older non-UEFI-PC (BIOS is from 2008), but it keeps giving me the error:

Windows cannot install required files. The file may be corrupt or missing. Make sure all files required for installation are available and restart the installation. Error code: 0x80070570

I used Rufus with the option MBR/BIOS (UEFI-CSM) to make a bootable USB stick with an official ISO file from Microsoft (I calculated the SHA1 hash of the ISO and it should be fine - see https://www.heidoc.net/php/myvsdump_details.php?id=P1503F62201Ax64Lde).

After the installation failed, I checked the setupact file which said Windows\WinSxS\wow64_microsoft-windows-wmi-core-providerhost_31bf3856ad364e35_6.3.9600.17415_none_0bc263c493833ebe\WmiPrvSE.exe was corrupted, so I figured out sources\install.wim on my USB stick might be corrupted and I compared its SHA1 hash with another install.wim file I had received by extracting the ISO file (using WinRAR) - the hashes were indeed different.

I then replaced install.wim on my USB stick with the other install.wim file (the hashes are now the same) and tried again - without success. I still get the same error, setupact now says: Calling WIMApplyImage (flags = 0x180)... [...] file corrupted [...] E:\Windows\WinSxS\wow64_microsoft-windows-i..-wow64-setupdll001f_31bf3856ad364e35_6.3.9600.16384_none_dd2bbcb0858e0596\_setup.dll (Error = 1392)

The PC now runs Windows 7 Enterprise, which was previously installed using the same method (Rufus, official ISO, MBR, etc.). Any help is highly appreciated.

Burning the image onto a CD (can be done with Rufus, too) instead of using a USB stick solved the problem in the end.