My monitor had a flickering issue. I couldn't rectify it through refresh rate changing.
So I purchased a new LCD monitor. Still, the issue persists.
What is the issue? Is it the problem of motherboard? How can I solve it?
Its probably a buggy video adapter. What you can do is get a really cheap PCI video card (as low as $10) just to see if that cures the problem. If it does, replace the motherboard (I'm assuming this is on board video), or get a better replacement video card .. or use the one you bought if it suits your needs.
Since it sounds like you now have two working monitors, you could get two cards and go for a dual headed display.
Ensure the cable connecting your monitor to the computer isn't defective. Jiggle the cable and see if the flickering changes. Could be a bent pin in one of the plugs on either en
Try each of the available display resolutions available to you and see if one of them causes the flickering to stop.
Does the flickering occur during BIOS boot up screens? If not, it's not a physical issue with the motherboard or graphics card. Try updating your video drivers, and checking for background-running programs that might be trying to put stuff on the display. It's possible you may be infected with some weird malware or virus as well.
If the display starts to flicker after the PC has been on a while, overheating may be a culprit.
Other than this, it's likely a hardware level issue and you should get a qualified PC technician to open the PC and inspect for possible physical/liquid damage, or other anomalies.