A 37 inch insignia tv won't turn on after i plug my laptop for some music.then after unplugging my laptop it won't turn on.please give me best possible answer.( tv is about 2 years old)

This is the basic guide that can be applied to most LCD flat panel TV.

First, try unplugging it from the outlet for about an hour to see if the TV will reset itself since the minute the TV is plugged into the wall, the power supply and processor will be running 24/7 and the EPROM can get corrupted by spikes and surges. Try using good quality surge suppressor to see if it will help if it happen often.
Look for burnt brown hot spots on the circuit boards, capacitors with leaking/bulging top or seals. Loose wires and connectors. Blown fuses.
Notes: We are dealing with high voltage that can kill you! so if you are not sure what you are doing, please have it fixed by the pro that has proper tools and safety equipment. Try to use GFI outlet and isolation transformer when work around the TV set and DO NOT DEFEAT THE GROUND PIN OF THE OUTLET/POWER CORD.

1)The power supply module (There are 4 regulated output voltages:- Standby 5vdc, switched 5vdc, 12~16vdc, and 24vdc).

The power supply converts the 120/230vac 50/60Hz into DC, then the high frequency (50~100kHz) switching circuits convert it back to AC but at high frequency which allows the power supply to use smaller and much lighter weight transformers (Ferrite core instead of heavy iron core), then this high frequency AC voltage is fed to the rectifier Diodes to get the DC output and filtered by DC filter capacitors that must have low ESR (Equivalent Series Resistance), if general purpose electrolytic caps are use, they will fail within a year or less due to high ESR.

The power supply has Standby 5vdc (5VSB, this is a MUST have before anything else will work, when this voltage is not present, there will be no any indicator light on the front panel) which is always on the minute the TV is plugged into the AC outlet, so it is on 24/7 and that is why the power supply will fail even though you may use the a TV not very often. It will see all the voltage spikes and surges 24/7.
This 5vdc is used to power the Processor and the Infrared remote receiver module which will be waiting for the command from the remote control or from the power switch, when the Power on command is received, the Processor will send the turn on signal (3.3~5vdc) to the power supply module (PSON pin) to the switch on the main 5vdc for the rest of the logic and Tuner circuits, 12~16vdc for the sound amplifiers (mostly Class D amplifier for efficiency and small size) and for the T-CON board (interface board between the LCD panel and the Logic board), and 24vdc for the Back lights inverter board (if there is no 24vdc then no back light).
Common failures:
Blown main AC fuse due to shorted out Diodes, transistors.
Bad capacitors leaking or bulging tops:
Shorted Diodes, transistors in the DC output side.