Which of your 3 monitors is the Primary? Is it the Dell E2310H? If so, remove that monitor from the 680 card, and make the other Dell or the HP monitor the Primary and get it working with 2 monitors. Once that works, try the Dell E2310H as the 3rd monitor and see if that works? If it does, that 680 card may have some driver incompatibility with the Dell E2310H monitor. Did you download the latest driver from Dell for the Dell E2310H monitor?
Also, you might try the Dell E2310H on another desktop PC or laptop that you know works properly with an external monitor. Does that monitor work properly an another computer? If it does, you could be looking at driver problems with the 680 card.
If the Dell E2310H monitor fails to work...