Helping people with computers... one answer at a time.
An upgraded computer may shut down because the existing power supply isn't strong enough. Here's why.
Sounds like you've upgraded your machine quite nicely. I'm guessing it runs much faster, and much smoother.
Until it dies, of course.
There's one component you didn't upgrade that I suspect as being the likely cause of your problem.
Most people consider the CPU to be the heart of the computer. I don't look at it that way. The brains, maybe, but not the heart.
Your power supply is the true heart of your PC. Quietly, or not so quietly, pumping out electricity at the various voltages required by the various components of your computer, the power supply is an often over looked, and under appreciated component. I mean, when was the last time you saw anyone get excited about a power supply?
With the changes you've made, it's likely that your new computer is drawing more power than your old one, and it's quite possible that your power supply isn't keeping up. It could easily be overheating and shutting down after you use it for a while.
You mention that it's the "old casing with one fan". Chances are that one fan is on a small box and that small box is your old, probably tired, power supply. That would be my first guess, and the very first thing I would replace. It's probably rated for some number of watts - I'd now get one at double that rating.
The other thing that your new components are probably doing is also generating more heat. It's possible that your power supply is ok, but that one fan isn't enough to keep the motherboard and other components from overheating. This is relatively easy to test ... keep the cover off of your computer, and get a table-top fan to blow air at it. If it stays running, then one way or another, you're probably overheating when the box is closed.
The solution may well be the same. That more powerful power supply I mentioned above may well include a more powerful fan capable of moving more air. Alternately, you might see if you can mount a second fan in your case to help move air through.
There's also a small chance that the problem is only the CPU overheating. If it doesn't already have a fan mounted directly on or over it, you might look into adding that as well.
Your new motherboard probably has thermometers in various places to help measure the state of various components. Check out Motherboard Monitor, a free tool that will report your CPU's temperature among other things. It's a tad geeky, but there's good information.