Most likely culprits are memory and PSU. Before we start standard troubleshooting (pulling the system down to bare essentials and building one by one and testing after each addition), you probably want to test the worse case scenario first (a bad PSU), because if this thing fries, you can take out a number of hardware devices.
PSU testing will require you to free up a 4-pin molex and your aux so they are within testing reach, as well as breaking out a good multimeter, I prefer digital with small probes for computer work.
12v: Put red probe in yellow wire, black probe in black wire of 4-pin molex.
5v: Put red probe in red wire, black probe in black wire of 4-pin molex.
3.3v: Put red probe in orange wire, black probe in black wire of aux.
When I say wire, I mean the actual plug that the wire ends at, not jabbing the probe into the wire sheath
. Generally, you want to test your voltages at all stages of computing (at POST, in BIOS, when Windows starts up, shuts down, idle, under load, etc...). At any stage, your voltages should be within the following ranges:
3.14V to 3.47V
4.75V to 5.25V
11.4V to 12.6V
If you go above or below these standard ranges, it means your PSU isn't falling within the specifications for an ATX PSU. Computer hardware is built to operate within these ranges. Any PSU that is out of these specs should probably be replaced or 'unloaded' (remove hardware) until they are within range. If you have to unload your PSU, you need a better one, because it just doesn't have what it takes to power your system.
Once you know your PSU is safe, you could run a quick Memtest overnight and report back if it found anything.
<--unzip and burn image to a CD.
If memtest comes back with an error, remove all but one stick and test again- and keep doing this per memory until you determine which is the bad stick. If they all pass a night of torture, you can probably rest assured it's not the memory.
So if it's not the PSU or the RAM, I would look to blown capacitors on your motherboard (another common problem). They are easily distinguised because they have a halo of chemical residue either bursting from the top of them or blown on the motherboard beneath. They can also bulge (meaning they are about to blow). Capacitors regulate voltage and can essentially cause the same exact instability that a PSU causes. If they are expired, they will cause ****.
Once you test those three, you can start disassembling your computer and rebuilding it from scratch, testing stability after each installed device. You want to test under load. If you install a device and your computer starts acting up, you have a good idea which device it is, and you can replace it. Since your computer is under a year old, each part should be covered by warranty unless you bought refurbished parts. So good news is, this shouldn't cost you any more than a few bucks to fix (pay for shipping, RMAing old part).