[Build Help] Upgrade Processor or Graphics Card?

Hello,

Here is my current build: PCPartPicker part list / Price breakdown by merchant

Type Item Price
CPU Intel Pentium G620 2.6GHz Dual-Core Processor $67.99 @ Mac Mall
Motherboard ASRock H61M-DGS Micro ATX LGA1155 Motherboard $49.99 @ Mwave
Memory Crucial Ballistix 8GB (2 x 4GB) DDR3-1600 Memory $82.99 @ Newegg
Storage Samsung 840 Pro Series 128GB 2.5" Solid State Drive $108.98 @ OutletPC
Video Card Sapphire Radeon HD 7950 3GB Video Card $228.99 @ SuperBiiz
Power Supply Corsair Builder 430W 80+ Bronze Certified ATX Power Supply $41.86 @ Amazon
Monitor Asus VS239H-P 23.0" Monitor $150.00 @ Amazon
Monitor Asus VS239H-P 23.0" Monitor $150.00 @ Amazon
Total
Prices include shipping, taxes, and discounts when available $880.80
Generated by PCPartPicker 2015-01-17 11:28 EST-0500

I built this computer incrementally. It started as a work computer and then I added the HD 7950 about a year ago. I started playing League of Legends around that time. However, I get serious FPS drops during intense moments of the game. I was wondering what CPU I should upgrade to for better performance. Also, is there anything else I should consider upgrading?

Finally, is it worth it to just overhaul the whole build and get a new CPU/GPU/MOBO/PSU/anything else, or is an incremental improvement the way to go?

Any thoughts would be helpful.

/r/buildapc Thread