To test RAM you would use MEMTEST86, from memory you get a boot option when you start slax where you can select that option, most modern distros do. In terms of checking your CPU what do you want? I'm guessing some form of stress testing to ensure it's working OK.
I'm buying new ram and looking at buying a new cpu (not sure yet), but don't know what I currently have (or how much). Because I'm still waiting for my replacement HD to arrive, I can't check normally (through windows). I tried using cpuz but realized that linux doesn't run executable files.
What I need is to find out how much ram my system currently has and what the cpu clock speed is...but have no idea how to check either in linux.
p.s. thanks for the memtest suggestion, I got all the info I needed about my ram, and then some