2nd Monitor Not working Dell Inspiron 3670

Do you only have onboard Intel Graphics 630 or do you also have an add-in (NVidia) video card ?

Graphics 630 should be able to run two monitors.

Will the one connected to VGA start working properly when the "main" monitor's HDMI cable is unplugged from the PC and you reboot?

What happens if the monitor connected VGA now is reconnected to HDMI on PC, after you disconnect the "main'" monitor that's currently connected to HDMI and then reboot?

If the "main" monitor has a VGA port, will it work when connected to PC's VGA, either alone or with the other monitor connected to HDMI?

Doing these swaps may help you figure out if this is an issue with the PC or an issue with the monitor that's been connected to VGA.

EDITED

try disconnect your primary monitor from integrated HDMI, connect the new Dell monitor to VGA.  In this way your PC has a single monitor on VGA.  Test for video.  If no video there, something wrong with the motherboard VGA port, or VGA cable/new monitor.  Test Dell monitor and VGA cable on another PC to r/o their issue.  If they work on another PC, then you narrow it down to 3670 VGA port have no video signal.

If single monitor on VGA has persistent good video, then the issue is with dual monitor set up.  It is not a power issue as monitors get their own power supply.  the Question is whether there are stable video signal on both HDMI and VGA.

Powered up today and 2nd new monitor connected to VGA was working.  Then there is some gainy intermittent lines, just flashes.  It stays on for many minutes using it as an extended display.  Then can go dark for less then a minute. 

So I unplugged HDMI from main monitor, moved the VGA input from 2nd to main.  Same behavior on main monitor.  A few intermittent gainy lines then dark for a few seconds.  Plugged HDMI into 2nd and it comes on with higher definition and solid.  No glitching.  Power off/on and same symptoms. 

Swapped VGA back to 2nd, HDMI back to main.  Powered off.  Reconnected VGA at PC, powered on.  Same symptoms on 2nd monitor. 

Perhaps this VGA cable that came with the new monitor is defective.  I will get a new one to try.  And perhaps the VGA port on the motherboard (which until now has never been used) has some problem. 

@NobleDesign  Sounds like you're narrowing it down to the PC.

What build of Win 10, eg 20H2, 21H1...?

Any signs of overheating?

Open Windows Event Viewer and look for any error messages around the time the 2nd monitor goes blank. That may point you toward the problem.

Are all your drivers up-to-date? There's a new Intel UHD Graphics driver update.

What version of:

• BIOS? Latest is 2.19.0.
• Intel Management Engine? Latest is 2110.15.0.2210 which "contains critical bug fixes and changes to improve functionality, reliability, and stability".
• Intel Graphics Command Center app? Latest version is 1.100.3325.0
• Etc

Scanned thoroughly for malware recently? Malwarebytes (free) is a useful tool.

What unnecessary stuff is running in the background and hogging system resources?

Does the same problem happen if you boot in Safe Mode?

Signs of overheating?  If in the beginning you don't know what to look for then I would have say don't know.  Having lowered the temperature of my shop from 93f, to 87f and now 81f in the course of 7 hours and watched the intermittent wavey lines and black outs on the 2nd monitor/VGA diminish to none I would have to say....yes, I believe I was seeing signs of over heating.  Not having had many computers I must say I am humbled at the findings.  My cell phones and never seemed to suffer from high temps but I have a whole new respect for PC's and their mother boards. 

Running 2 monitors with Intel UHD Graphics can put a load on the CPU and that will cause it to heat up...

Did you clean off the old thermal paste from CPU and heat sink, and apply fresh thermal paste before you installed the heat sink and fan on the new motherboard? Did you then connect the fan's power connector to the motherboard?

Reboot and start tapping F12 when you see the Dell splash screen.  When the F12 menu opens, select the option to run the diagnostics. Run all of them, including fan tests. Copy error messages, if any.  If you get a fan error, it will have to be replaced with a Dell OEM fan for this PC model.

I have 5 of them at the office with Bad VGA ports.   Have swapped cables, tried booting with just the vga, run Dell diagnostics and it tells me everything is fine...