LG RD405 MOTHERBOARD PROB.

Before you decide replacing the motherboard, have you determined the fault in the laptop?
I suggest you attach a monitor to the laptop and power up the monitor then bootup the laptop. This will automatically switch the video data to the external monitor. If you don't get a normal Windows image then you could have a faulty video card or faulty memory.
In a laptop the video card uses part of the main RAM (memory), try re-seating the RAM module/s and see if this corrects the problem.
If not you could have faulty RAM module/s, take them to your friendly computer repair shop and get them to test them for you. If these are OK then you definitely have a faulty video chip problem. This is part of the motherboard and the fix is a replacement motherboard.
Replacing the motherboard may not be a cost effective solution, but it depends upon the age of the laptop and the costs of repair.
If you decide to get a new laptop, you can salvage the hard drive from this laptop and insert it into an USB hard drive adapter case and use it as an external USB hard drive.