Need Help Balancing GPU with CPU/Mobo

[Stylis]

Hi all, so I recently upgraded my graphics card from an EVGA GTX275 to an EVGA GTX 780, superclocked to 1020 MHZ. I can't get high,stable framerates on intensive games like BF4 and Splinter Cell Blacklist, which from my understanding after research is most likely from bottlenecking from the CPU (my rig is moving onto it's fifth year). So what I'd like to ask is an ideal CPU/Mobo combo and a cost efficient CPU/Mobo combo to upgrade to (bundle deal maybe?) so that my CPU can fully utilize my GPU. I'm not the most savvy with speeds and compatibility but I believe in the community's knowledge (and I'm willing to learn)! Any assistance with this would be fantastic, thanks, and here's my current build:

CPU: AMD Phenom™ II X4 965 Black Edition
Mobo: [CrossFire] Asus M4A77TD PRO -- AMD 770/SB710 Chipset w/7.1 Sound, Gb LAN, S-ATA Raid, USB 2.0, Dual PCI-E MB
RAM: G.SKILL Sniper Series 8GB (2 x 4GB) 240-Pin DDR3 SDRAM DDR3 1866 (PC3 14900)
Power Supply: 750 Watt -- Corsair CMPSU-750TX Power Supply - SLI Ready
1 TB Hard Drive - [16M Cache, 7200 RPM, 3.0Gb/s]
Samsung EVO 256GB SSD
Thermaltake MaxOrb fans + stock NZXT case fan at the top
Nzxt Lexa Blackline Gaming Tower Case

Note: Looking to possibly SLI two GTX780's in the future so maybe I should get a bigger case too?

 

[vegetablegod]

Have you updated your drivers? Make absolutely sure...

nvidia drivers

 

[HiTechObsessed]

This would be a good upgrade:

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: AMD FX-8350 4.0GHz 8-Core Processor ($184.67 @ Amazon)
Motherboard: Asus M5A99X EVO R2.0 ATX AM3+ Motherboard ($104.99 @ Newegg)
Total: $289.66
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-03-03 16:44 EST-0500)

Would allow for overclocking and SLI in the future as well. Depending how old your PSU is, you would probably want to upgrade that before SLI though.