I disagree the r9 270 with 2 gb of vram will be a significant upgrade. I had a Radeon hd 6870 1 gb (better than a 650 ti) and I noticed a huge performance boost from one to the other. I have two r9 270s and the only game I play where I actually need the second card is Crysis 3. I game at...
I would sell the 7850 on Ebay and get a r9 280 because unless the 7850 is the two gb version you will run out of vram before you run out of processing power.
You should be fine I have two r9 270's overclocked an i5 overclocked to 4.5 with 6 case fans an ssd and 3 mechanical drives on a 700 watt psu with no issues.
If you are going to go with sli 770s I would spend a little more and go with the a 3 or 4gb version. The problem you will run into with the 2gb versions is that you will run out of vram b4 you run out of processor power.
Put the old card back in run this program put the new card back in and install the new drivers and it should work. (If it is the same problem I was having)
http://www.guru3d.com/files_details/display_driver_uninstaller_download.html
This one is newer and better if you can spend the extra
http://www.amazon.com/AMD-A10-Series-APU-A10-7700K-AD770KXBJABOX/dp/B00H7Z7XA6/ref=sr_1_1?ie=UTF8&qid=1402940111&sr=8-1&keywords=AMD+A10-7700K