My Computer refuses to show on the monitor

I am using HP H8-1203 Intel core i7-2600, 3.4Ghz (8 CPUs) Tower PC with 8 GB RAM and 4.0GB NVIDIA GeForce GT 620 Graphic card. Please I want to know why my PC does not display image on the monitor when ever I boot my PC? Most times it show inactive screen on the monitor and will never display any image on the monitor and sometimes, luckily enough it comes on. I have used another monitor and it kept doing the same thing. I have unplug every hardware and fixed them back but to no avail. The system has no on-board VGA slot but I have bought a new graphic NVIDIA card to replace the initial one, yet I am still going through the same challenges. I have reset the CMOS battery and even changed the CMOS battery too. All my troubleshoot is floored. I've test my RAM and Hard drive and there are in good condition. What I notice is that my PC comes on when it chooses to come on and I'm fade-up of this processes. I'm tired of waiting for 2 to 3 days before having my system on. The most annoying thing is that the the System unit is on, the fans are on, the light are all coming on but it does not give signal to the monitor even when I have replaced both the monitor and the graphic card. Please can someone be of good assistance to me?