Why won't my monitor connect to new desktop with HDMI cord?

[GRETHEL]

Just purchase HP ENVY DESKTOP 750-435 st.  My specs:  I7-6700 Processor, 6th Generation, 16 GB DDR4, NVIDIA GeForce GTX 960, 256 SSD + 2TB HDD storage.   I have a monitor, that I have been using without any issues:  HP Pavillion 25bw.  When I tried to connect the HDMI cable to either HDMI 1, or HDMI 2 port, it would not connect.  The monitor did not receive a signal, and immediately went to Sleep mode.  However, when connecting it to the other HDMI ports, it did.
 
I am concerned because I want to get the most out of the Graphics card.  Also, the computer came already with a name, which is making me wonder, if this was a return, and the prior person was having the same issue.  This is my third day having this desktop, so I am within the time frame to return it; though I do not want to.  However, I am not a tech savvy person, to be opening computers to fix this issue.
 
Am I being unreasonable in expecting a very expensive computer to work out of the box?

[banhien]

@GRETHEL

Welcome to HP Support Forum. Your machine has the following ports at its back:

Figure : GeForce 960 ports

1. DisplayPort: 3
2. HDMI
3. DVI-I

and

Figure : Odense2-S back I/O panel

1. USB 2.0: 2
2. LAN (Ethernet)
3. HDMI
4. USB 3.0: 2
5. Audio: Line in
6. Audio: Line out
7. Audio: Microphone

Source:  https://support.hp.com/rs-en/document/c05267115

The first image is for an external card and the second image is for the motherboard which has 2 HDMI ports for the Integrated video. But please note: Integrated video is not available if a graphics card is installed.

Therefore you can't use  2 ports of the Integrated card. But you have plenty of DP ports to connect monitors. If your monitor(s) does/do not have DP ports, you can use DP to HDMI cable(s).

Regards.

[GRETHEL]

So I  believe then that I connected it correctly.  I thought that I needed to use what is on figure 2, and connect the HDMI cable on either port that is labeled HDMI 1 or HDMI 2.  It added to confussion because it was labeled, and for a non techie person, it threw me off.

Can you tell me, if the computer was named when I got it, is is safe to presume that it was a returned PC?  As long as it all working, I am ok with it.  It came with a nick already, but is small and I can leave with that.