1. put the old parts back in
2. run the programs that caused crashes
3. if still crashes, run a temp monitoring program and check the temps. you might have knocked a bit the heatsink off the CPU and not even noticed... Also, suggest run Memtest as well.
4. If it runs fine, replace the PSU first and rerun the tests. If crashes, you know PSU is bad.
5. if fine, replace the graphics card and rerun the tests. If crashes, the card is bad.
Every time ensure no power cables are disconnected by mistake, the heatsink is still firmly in place along with the rest of the hardware (mem sticks, other cards, cables to/from HDD, etc.).
In my experience, the 4xx cards series had a heating problem, and it may be that to blame, given the symptoms you reported already. I suppose the card is properly fed with power and you didn't miss any additional power connections to it.