Various programs are crashing with an access violation (0xc000000d). What's wrong?

For a few months now, various unrelated programs have been periodically crashing on me. This seems to happen more often when a program has been open a while, versus just opening and closing it within a short timeframe. What's interesting is that all of the crashes have the same offset, specifically 0x77xx4b41, which corresponds to where ntdll.dll is loaded.

A selection of programs where this occurs:

• Adobe Reader
• eM Client (a managed .NET 4 executable)
• iWrap.exe (the Intel PROset profile migrator thingy, it crashes when you hit cancel on the dialog to select a profile to import)
• Proxmon.exe and AccessEnum.exe (Sysinternals tools)
• windbg.exe
• ...and others.

My machine is Windows 10 32-bit with 4GB RAM, upgraded all the way from XP ("do a fresh install" is not an answer I will accept). There are no hardware problems that I know of, and memtest86/chkdsk/dism/sfc all come back clean. How do I find out what's causing this?