OK. So the monitor works. At the rear of the PC are there two sets of video outputs? You might have a dedicated graphics card installed and that will disconnect the motherboard's GPU output. Something easily overlooked. You might have connected to the wrong port, possibly.
If desktop VGA outputs worked with old monitor (from reading your post), and not working (not touching the PC end) when VGA is plugged to new monitor. And new monitor is working with laptop. Then I would change the graphics card of the PC to default settings using a common resolution and check that output Monitor 1 or 2 is pointing to the correct one. Graphics card with multiple ports output to multiple monitors.
This thread is now locked and can not be replied to.