Hello and welcome to JustAnswer! I am Pete, a TV expert, and I'm happy to assist with your question today.
How old is your LG 37LB4D TV?
What color is the flashing light?
Have you left the TV turned off and unplugged from the power supply for 30 minutes, then tried turning it on again?
And after this reset, it still has the same problem?
Ok, this indicates that the power supply board inside your TV is not working correctly.
Sometimes a reset can correct the problem, but if it still fails to turn on then the power supply board will need to be replaced.
A replacement board will cost around $100, and around $50-100 labor for fitting it, if you cannot fit it yourself.
Here is the board you require: http://www.partstore.com/Part/LG+Electronics+Incorporated/LG+Electronics%2fZenith/EAY33058501/New.aspx
Not too hard if you have some technical experience - you will need to remove the rear panel off the TV, then unscrew the old board and remove the cable connections from it. Take the old board out and fit the new one in its place, then screw it in and connect the cables again.
It's a time-consuming job and should take around two hours to complete.
Yes, it is a common problem with all modern LCD TV's.
The components used on the power supply board can fail after a few years of use.
Glad I could help.
Thanks for using JustAnswer!