|I agree with both.|
Always test before replacing.
Always test memory before testing hard drive because a memory error could cause false readings, segments marked bad that are actually good, and other problems.
Test memory with Memtest.
Test hard drive with your hard drive manufacturer's utility or Seagate Seatools (since it works on nearly all drives).
Windows Install Disks ARE fine for partitioning and formatting your disk before installing for all normal conditions. There are some advantages with using some other software to do the initial partition/format, but for most who use one or two partitions on a drive, there is no significant difference.
This really DOES sound like your memory is bad so do that test first. Let it run through ALL tests. NO errors are acceptable, rerun with one stick at a time to confirm the bad stick and try the good one in both slots (if your motherboard lets you) to confirm the slot is good. Replace as needed, replace dual channel as a pair.
You have to be a little bit crazy to keep you from going insane.