Suppose the answer changes based on who you are buying from. A lot of these things either work or they don't...
HDD - you could use something like
Crystal Disk Info and hope everything shows up green. Or run a Long DST with Seatools (will take 5+ hours on large disks)
GPU - Visually inspect that it is clean, if possible have them run some benchmarks on it and monitor the temperature to make sure its reasonable and there is not artifacting or crashing happening.
Processor - If its less than 7 years old and hasn't been heavily overclocked it has an extremely high chance of being fine.
Motherboard - This is probably fine too if it is shown to work at all, check the caps to see none are bulging or leaking.
RAM - Nothing quick you can do here, ask them if it has passed multiple passes of memtest, you could have them show you, but it will take at least overnight before you get a real answer.
DVD Drive - if it burns disks and reads its fine. If it dies on you, not much you can do, things are like $16 new anyway, don't put a lot of thought into this.
PSU - just find out what one it is and google if it is any good. This really depends on how demanding your system is.
Basically you just have to have a little faith in who you are buying from and ask them if something doesn't work right away if you can return it.
