BSoD during Defrag

I have a Dell Inspiron 3000 in which I got a BSoD during defrag. Now, before the BSoD I did just added more memory (which is the right memory) as well as a 500GB WD HDD which I cloned the old drive to. I can't tell you if there's ever been another BSoD because this PC isn't mine but I can tell you it's running the Disk Check right now and checking for bad sectors as well as file system errors. That's the best solution I could come up with before I have to put the old hardware back in.

What do you guys suggest?

Thanks!