You seem to be stuck between a rock and a hard place.
We have tried with the open source nuveaou driver = No go
The new nvidia 331 and nvidia prime = still No go
I think it must be the old code base from Ubuntu 12.04 that's causing the trouble.
I would recommend you to try elementary OS Freya instead but I can't do it officially because it's in beta.
But if you are willing to be a beta tester like me it's completely up to you. It has a UEFI bug though so it might not work either.
The best option, until Freya is released, might be Ubuntu 14.04 for you
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