Dell 8 beep display problem VGA output

I own a Dell N5010 since 3 years. It's not covered by warranty at present. Recently it started showing the 8-beep problem. The system would turn on but there would be no display (not even the boot screen). Interestingly, after about 10 days it started normally just like that and worked as usual for about 15 days. Now it's again gone with the same problem.

On connecting the laptop with an external display (desktop monitor) it's working perfectly. This indicated that the motherboard was fine and that there was some problem with the LCD.

I contacted a local vendor and we supposed it to be an LCD problem, but then he said he tried my LCD with a different motherboard and it worked fine, so there was no defect in the LCD or connecting wires. He instead said there is some problem with the VGA output port and the motherboard needs to be repaired.

I am confused a lot and not able to pin-point the problem. Kindly help me decide. Should I go for repairing or order a new motherboard? Can anyone give me an idea about what the exact problem might be? Thanks.

Also note that my system overheats a bit. Could this be a result of the overheating?