I recently UPGRADED the CPU yesterday and the computer was running in perfect condition yesterday and today. I was playing a game and about a minute after I was done playing the game and was exited onto my desktop... my computer powered off.

So I waited about 30 seconds and turned it back on... it didn't turn on. The speaker that will beep never beeped- and the only thing that happens is the LED lights will dimly turn on. I had to turn my PC off by flicking the switch on the power box in the back. But no display- no nothing. The only fan that will turn when it is on is the rear fan and it barely spins. Aside from that- only LED lights from my fans will turn on and its dim. Is it a power box failure?

My computer is custom built!

NEWEST CPU: AMD FX 8350 (Previous one was a 6200)
Motherboard: Gigabyte GA-970A-UD3
RAM: Crucial Ballistix SPOT 16GB
Storage: WD RE2-GP 1TB 3.5" 7200RPM
GPU: Sapphire Radeon HD 7870 GHz Edition 2GB GDDR5
Case: Sentey GS-6400 Arvina ATX Full Tower
Windows 7 Home Premium

I only know my power supply is 550W. I had a PC repair place swap the one I have now with one that was defective back when I was building the thing and had issues.Have you tried putting the old CPU back in?
The new CPU may have failed.
Maybe you have to CHECK your motherboard again.What make and model of power supply is in the system?  This should be on a sticker that is stuck to the PSU itself.