This does sound like a hardware problem:
- Find the motherboard brand/model # and memory brand/model.
- Check the motherboard's manufacturer's support page for compatible memory with that specific motherboard. Also check their forum for similar problems and solutions.
- Unplug all non-critical peripherals ( might be a driver issue).
- Swap the two (or more) memory sticks, see if that changes the freezing somehow.
- Check mother board manufacturer for updated BIOS, especially if the new BIOS addresses memory concerns.
- If the BIOS doesn't have a memory test, Try MemTest86+.
- If it's not the hardware, the BIOS, or the BIOS settings: Boot a live USB stick, see if the problem still exists ( might be a corrupt install somewhere; backup data and install a different distro; on a different drive if available; or stick (a backup of?) the boot drive in a different machine).
- Dig into the logs, as mentioned elsewhere.