Memory Issues on new Setup

[Pure Blank]

First of all, thanks for taking your time to read this.
A week ago, i transferred my HDD with the Windows 7 installation along with 8 GB of RAM and the PSU to a completely new motherboard.
Since my download rate is only 240kb/ps, i didn't want to go through the trouble of re-downloading my whole library of games, movies and music of over 500 GB.
So i installed all the drivers for my new graphics card and the drivers for the motherboard and the CPU after rebooting on the new system.
Except for the slow booting, everything was fine at first.
Games like Crysis 3, Tomb Raider, Far Cry 4, Metro 2033 Redux and Final Fantasy 14 ran on highest settings with more than 30 fps.
While playing Far Cry 4 2 days ago, i noticed weird hick-ups and stutters, up to the point where it became unplayable and a window popped up, asking me about memory leaks.
When i rebooted my System, everything was fine again.
Today, Final Fantasy 14 crashed twice, a window saying that the game closed in an unusual way.
I noticed that the Games start to slow down when my computer has not been rebooted in 2 days.

People have told me to re-install Windows 7 to have a completely clean set up, to make everything run smooth and to shorten the booting times, but i was hoping to avoid this, due to my slow download rate :/.

Does anyone know what is causing the memory leak, or the system slow-down ?
I dont know exactly what it is, so please don't blame me for my speculations.



Edit: System Specs:

Motherboard: MSi 970 Gaming
CPU: AMD FX 6350
GPU: Sapphire R9 280 Dual-X
RAM: 8 GB
PSU: Vengeance 600W
Running on Windows 7 Home Premium 64bit

 

[LMiller7]

Post a screenshot of Task Manager - Performance tab when the problem occurs.

 

[Pure Blank]

That will be quite difficult, since it freezes my PC to the point where things take their time to react.
But i'll try.

I dont know if this is relevant, but UPlay used to freeze my PC up the same way before the hardware upgrade.
Everytime on log in and starting up a game, UPlay would freeze my PC completely for a period of time, but after that everythings just fine.