Ok so I've actually already made a list of what new hardware I'm getting. I should have said that in the thread.
New GPUS: 2x 760 GTX SLI
New CPU: The cheapest one compatible with the motherboard was the FX-6300, but I don't know if it would bottleneck the GPU's, if it does not, please let me know, as it is actually the only part I am unsure of whether or not to switch out.
New Motherboard: Gigabyte GA-990XA-UD3, Socket-AM3+ (Which means it would be the easiest to get the cheapest AMD CPU that will not bottleneck 2 GTX 760's)
New PSU: Cooler Master B700 700W
This is all the absolute cheapest, while still being compatible with everything else that I could find.
I also looked up benchmarks of 2 760 GTX's up against a 780, they were alot better than the 780 in almost all the benchmarks. In the games I will play, the 2 760's will get 10-30 FPS more than the 780. Of course, getting the 780 will be alot easier for me, as I know exactly what I should get, no worries about compatibility, but it's somewhere around the same price as the other rig (listed above)
Take to note, that I live in Denmark, and the hardware is most definitely more expensive, it's not gonna help anything by mentioning prices or budgets, I definitely just went for the cheapest, that is still efficient and compatible.
Eduello: Motherboard is mentioned above of this post
13thmonkey: As mentioned above in this post, I found benchmarks of 2 GTX 760's outperforming the 780.
GhislainG: Would the Cooler Master B700 be good enough? Again, I might not be able to find any cheaper and still compatible PSU in Denmark. I am ordering all my parts from one webshop, they are going to send it all in one package, which I find very very efficient, as I am a type of guy that is a little impatient, and likes everything as simple as possible.
AnEwG: As mentioned above in this post, I would have to change my entire rig, just to get an i5, and might just end up exceeding my budget (due to having to get another motherboard, remember, I listed the cheapest possible for me) but thanks for the advice.
PS. Yeah you might find a part that is cheaper and compatible with the rig, but remember, I found the absolute cheapest that I could find here in Denmark, so do not recommend me any cheaper and compatible parts to the rig.