First proplem i'd suggest doing the following.

Run 3D Mark 2001 or 2003 and see if the system locks. If it's a problem with graphics card that should course it to crash. Also take your side panel off whilst it's running so you can see if the cards fan is going round and if it's going at a fast enough speed to keep the card cool.

If all seems ok, i'd suggest removing all the PC's components and re-seating them, including the CPU.

As for the second problem. I'd suggest you don't bother using stanby mode. In my experiance it's twitchy as hell. Just turn your pc off if your leaving it.