Help Needed With Using Two Monitors: Optiplex 760 Desktop

Hello,

I am new to the Community.  Please forgive my technical naivety.  My knowledge of computing is limited.

I have an Optiplex 760 desktop. I believe it is a basic model with 4GB RAM and just the basic integral video card.  It's on its last legs (I'm getting the battery message on start-up) but it does fine for my needs, which is word processing, Excel, sending and receiving e-mails in Outlook and business-related internet use.

What I am trying to do is set up two monitors, so that I can have two different displays on at the same time - for instance, Outlook on one monitor and Word on another.  I have done this before.  About 10 years ago, I used an HP desktop in the same way and it was very easy.  All I did was connect two different VGA cables and it worked automatically.

Unfortunately, I am struggling to make the same idea work on this Dell desktop.  I have tried different monitors and different connection types and I now know more about display cables than I would have thought healthy for a normal person.  

The monitors have VGA and DVi ports and the Optiplex 760 has VGA and DP ports, and I have tried all the combinations with adaptors and hybrid cables.

VGA-DVi combinations with both hybrid and adaptor to DP don't work and I am left with only the VGA to VGA monitor working in that set-up.

VGA-DP combinations result in neither monitor working, even though one monitor is still connected as VGA to VGA in that set-up.

I have tried swopping cables between monitors.

To emphasise: both monitors power up and function fine as VGA to VGA.  

Neither monitor is Dell and I am not using Dell-branded cabling. 

A VGA splitter does work for two monitors, by the way.  That is no use to me, obviously, but it is of some relevance in that it does suggest the problem isn't the use of multiple displays, as such, so may be a cabling rather than software problem.

My own thoughts on this are that there are three possible explanations:

(i). One or more cable combinations I have tried should have worked but the cable(s) is/are faulty.

(ii). The DP port on my Optiplex 760 desktop is faulty.

(iii). My Optiplex 760 desktop will only tolerate one display cable at a time (albeit will accept a VGA splitter).  

Solutions seem to be either try Dell-branded cable or buy Dell monitors, ensuring they have DP ports.  Otherwise, if fault is with the desktop itself, a new desktop is needed if I want multiple different displays.

Can anybody add anything to this and make any recommendations? 

Can anybody recommend specific Dell monitors or cables or other solutions?

Frankly this is not my domain and any help would be appreciated.